Question

the initial population of a town is 17,000, and it grows with a doubling time of 10 years. what will the population be in 8 years? in 16 years?

what will the population be in 8 years?
(round to the nearest whole number as needed.)

what will the population be in 16 years?
(round to the nearest whole number as needed.)

Explanation:

Set up the exponential growth model

Using the Exponential Growth and Doubling Time knowledge points

$$ P(t) = P_0 \cdot 2^{\frac{t}{T_d}} $$

$$ P_0 = 17000, \quad T_d = 10 $$

$$ P(t) = 17000 \cdot 2^{\frac{t}{10}} $$

Calculate the population in 8 years

Using the Exponential Growth knowledge point

$$ P(8) = 17000 \cdot 2^{\frac{8}{10}} = 17000 \cdot 2^{0.8} $$

$$ 2^{0.8} \approx 1.741101 $$

$$ P(8) \approx 17000 \cdot 1.741101 \approx 29598.72 \approx 29599 $$

Calculate the population in 16 years

Using the Exponential Growth knowledge point

$$ P(16) = 17000 \cdot 2^{\frac{16}{10}} = 17000 \cdot 2^{1.6} $$

$$ 2^{1.6} \approx 3.031433 $$

$$ P(16) \approx 17000 \cdot 3.031433 \approx 51534.36 \approx 51534 $$

Answer:

Question 1

What will the population be in 8 years?
<blank>29599</blank>

Question 2

What will the population be in 16 years?
<blank>51534</blank>