Question

The population in Smalltown in 2010 was 47,597 people and is growing exponentially at a rate of 1.8 percent. Which of the following equations defines the population t years after 2010?​

Answer 1

Given Information:

Starting population = P₀ = 47,597

rate of growth = 1.8%

Required Information:

Equation that defines the population t years = ?

Answer:

The following equation defines the population t years after 2010.

$P(t) = 47,597e^{0.018t}$

Step-by-step explanation:

The population growth can be modeled as an exponential function,

$P(t) = P_0e^{rt}$  

Where P₀ is the starting population in 2010, r is the rate of growth of the population and t is the time in years after 2010.

We are given that the starting population is 47,597 and rate of growth is 1.8%

So the population function becomes

$P(t) = 47,597e^{0.018t}$

Therefore, the above function may be used to estimate the population for t   years after 2010.

For example:

What is the population after 10 years?

For the given case,

t = 10

$P(10) = 47,597e^{0.018(10)}$

$P(10) = 47,597e^{0.18}$

$P(10) = 47,597(1.1972)$

$P(10) = 56,984$