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
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.

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.

Relevant Questions

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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.
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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 $$\sigma_2 = 13$$.
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At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
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At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
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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.
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