The exponential growth function for the given situation in which the growth factor is the sum of 1 and the growth rate:
\(\displaystyle{50}{\left({1}+{0.15}\right)}^{{x}}\)

Question

asked 2021-02-03

From 2000 - 2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008.

a) Exponential growth or decay:

b) Identify the initial amount:

c) Identify the growth/decay factor:

d) Write an exponential function to model the situation:

e) "Do" the problem.

a) Exponential growth or decay:

b) Identify the initial amount:

c) Identify the growth/decay factor:

d) Write an exponential function to model the situation:

e) "Do" the problem.

asked 2021-01-06

Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. The student enrollment in a local high school is 970 students and increases by 1.2% per year, 5 years.

asked 2021-02-24

Consider the following case of exponential growth. Complete parts a through c below.

The population of a town with an initial population of 75,000 grows at a rate of 5.5% per year.

a. Create an exponential function of the form

\(Q=Q0 xx (1+r)t\), (where r>0 for growth and r<0 for decay) to model the situation described

The population of a town with an initial population of 75,000 grows at a rate of 5.5% per year.

a. Create an exponential function of the form

\(Q=Q0 xx (1+r)t\), (where r>0 for growth and r<0 for decay) to model the situation described

asked 2020-10-23

The close connection between logarithm and exponential functions is used often by statisticians as they analyze patterns in data where the numbers range from very small to very large values. For example, the following table shows values that might occur as a bacteria population grows according to the exponential function P(t)=50(2t):

Time t (in hours)012345678 Population P(t)501002004008001,6003,2006,40012,800

a. Complete another row of the table with values log (population) and identify the familiar function pattern illustrated by values in that row.

b. Use your calculator to find log 2 and see how that value relates to the pattern you found in the log P(t) row of the data table.

c. Suppose that you had a different set of experimental data that you suspected was an example of exponential growth or decay, and you produced a similar “third row” with values equal to the logarithms of the population data.

How could you use the pattern in that “third row” to figure out the actual rule for the exponential growth or decay model?

Time t (in hours)012345678 Population P(t)501002004008001,6003,2006,40012,800

a. Complete another row of the table with values log (population) and identify the familiar function pattern illustrated by values in that row.

b. Use your calculator to find log 2 and see how that value relates to the pattern you found in the log P(t) row of the data table.

c. Suppose that you had a different set of experimental data that you suspected was an example of exponential growth or decay, and you produced a similar “third row” with values equal to the logarithms of the population data.

How could you use the pattern in that “third row” to figure out the actual rule for the exponential growth or decay model?

asked 2020-12-24

Write an exponential function to model each situation. Find each amount after the specified time. A population of 120,000 grows \(1.2\%\) per year for 15 years.

asked 2021-01-19

Write the exponential growth function to model the following situation:

A population of 422, 000 increases by 12% each year.

A population of 422, 000 increases by 12% each year.

asked 2021-03-11

Tell whether the function represents exponential growth or exponential decay. Identify the growth or decay factor.
\(\displaystyle{y}={0.15}{\left(\frac{{3}}{{2}}\right)}^{{x}}\)

asked 2021-03-02

Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. A new car is worth $25,000, and its value decreases by 15% each year, 6 years.

asked 2021-02-05

The value of a home y (in thousands of dollars) can be approximated by the model, \(y= 192 (0.96)^t\) where t is the number of years since 2010.

1. The model for the value of a home represents exponential _____. (Enter growth or decay in the blank.)

2. The annual percent increase or decrease in the value of the home is ______ %. (Enter the correct number in the blank.)

3. The value of the home will be approximately $161,000 in the year

1. The model for the value of a home represents exponential _____. (Enter growth or decay in the blank.)

2. The annual percent increase or decrease in the value of the home is ______ %. (Enter the correct number in the blank.)

3. The value of the home will be approximately $161,000 in the year

asked 2020-10-23

Determine whether each function represents exponential growth or decay. Write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay.

\(y=450 \cdot 2^x\)

\(y=450 \cdot 2^x\)