Solve the given problem related to population growth. During the first decade of this century the population of a certain city grew exponentially the population of the city was 146210 in 2000 and 217245 in 2010. Find the exponential growth function that models the population growth of the city use t= 0 to represent 2000 and t= 10 to represent 2010 and so on. N(t)=? Use your exponential growth function to predict the population of the city in 2016. Round to the nearest thousand.

Solve the given problem related to population growth. During the first decade of this century the population of a certain city grew exponentially the population of the city was 146210 in 2000 and 217245 in 2010. Find the exponential growth function that models the population growth of the city use t= 0 to represent 2000 and t= 10 to represent 2010 and so on. N(t)=? Use your exponential growth function to predict the population of the city in 2016. Round to the nearest thousand.

Question
Exponential models
asked 2021-01-16
Solve the given problem related to population growth.
During the first decade of this century the population of a certain city grew exponentially the population of the city was 146210 in 2000 and 217245 in 2010. Find the exponential growth function that models the population growth of the city use t= 0 to represent 2000 and t= 10 to represent 2010 and so on.
N(t)=?
Use your exponential growth function to predict the population of the city in 2016. Round to the nearest thousand.

Answers (1)

2021-01-17
Let the exponential growth function is, \(\displaystyle{N}{\left({t}\right)}={N}_{{0}}{e}^{{{k}{t}}}\)
where \(\displaystyle{N}_{{0}}\) and k are the arbitrary constant and t is time.
Since it is given that at t=0 the population of the city was 146,210 so,
\(\displaystyle{146210}={N}_{{0}}{e}^{{{k}{\left({0}\right)}}}\)
\(\displaystyle{N}_{{0}}={146},{210}\)
Also it is given that the population of the city was 217,245 at t=10. so,
\(\displaystyle{217245}={146210}{e}^{{{k}{\left({10}\right)}}}\)
\(\displaystyle{10}^{{k}}={\frac{{{217245}}}{{{146210}}}}\)
\(\displaystyle{10}{k}={\ln{{\left({1.4858}\right)}}}\)
\(\displaystyle{k}={0.03959}\)
Hence, the exponential growth function will be, \(\displaystyle{N}{\left({t}\right)}={146210}{e}^{{{0.03959}{t}}}\)
Substitute t=1 to find the population in the year 2016,
\(\displaystyle{N}{\left({16}\right)}={146210}{e}^{{{0.03959}{\left({16}\right)}}}\)
\(\displaystyle={146210}{e}^{{{0.6335}}}\)
\(\displaystyle={146210}\times{1.884}\)
\(\displaystyle={275460}\)
Hence, the population of the city will be 275,460 in 2016.
0

Relevant Questions

asked 2021-03-07
This problem is about the equation
dP/dt = kP-H , P(0) = Po,
where k > 0 and H > 0 are constants.
If H = 0, you have dP/dt = kP , which models expontialgrowth. Think of H as a harvesting term, tending to reducethe rate of growth; then there ought to be a value of H big enoughto prevent exponential growth.
Problem: find acondition on H, involving \(\displaystyle{P}_{{0}}\) and k, that will prevent solutions from growing exponentially.
asked 2021-05-05

A random sample of \( n_1 = 14 \) winter days in Denver gave a sample mean pollution index \( x_1 = 43 \).
Previous studies show that \( \sigma_1 = 19 \).
For Englewood (a suburb of Denver), a random sample of \( n_2 = 12 \) winter days gave a sample mean pollution index of \( x_2 = 37 \).
Previous studies show that \( \sigma_2 = 13 \).
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
\( H_0:\mu_1=\mu_2.\mu_1>\mu_2 \)
\( H_0:\mu_1<\mu_2.\mu_1=\mu_2 \)
\( H_0:\mu_1=\mu_2.\mu_1<\mu_2 \)
\( H_0:\mu_1=\mu_2.\mu_1\neq\mu_2 \)
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference \( \mu_1 - \mu_2 \). Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are statistically significant.
At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
\( \mu_1 - \mu_2 \).
(Round your answers to two decimal places.)
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
asked 2021-01-31
The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume that the population grows exponentially.
(a) Find a function that models the population t years after 1990.
(b) Find the time required for the population to double.
(c) Use the function from part (a) to predict the population of California in the year 2010. Look up California’s actual population in 2010, and compare.
asked 2021-02-25
The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume that the population grows exponentially.
(a) Find a function that models the population t years after 1990.
(b) Find the time required for the population to double.
(c) Use the function from part (a) to predict the population of California in the year 2010. Look up California’s actual population in 2010, and compare.
asked 2021-05-26
You open a bank account to save for college and deposit $400 in the account. Each year, the balance in your account will increase \(5\%\). a. Write a function that models your annual balance. b. What will be the total amount in your account after 7 yr? Use the exponential function and extend the table to answer part b.
asked 2020-10-28
The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 18900.
(a) Find a function that models the population t years after 2000 (t=0 for 2000). Hint: Use an exponential function with base e.
(b) Use the function from part (a) to estimate the fox population in the year 2008.
asked 2021-01-05
The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 18900.
(a) Find a function that models the population t years after 2000 (t=0 for 2000). Hint: Use an exponential function with base e.
(b) Use the function from part (a) to estimate the fox population in the year 2008.
asked 2020-11-03

The exponential models describe the population of the indicated country, A, in millions, t years after 2010.Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
India, \(A=1173.1e^{0.008t}\)
Iraq, \(A=31.5e^{0.019t}\)
Japan, \(A=127.3e^{0.006t}\)
Russia, \(A=141.9e^{0.005t}\)

asked 2020-12-24
The half - life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days. Round your answer to the nearest thousandth.
asked 2021-01-02
The half - life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days. Round your answer to the nearest thousandth.
...