Question

the initial population of a town is 14,000, 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.)

Explanation:

Define the exponential growth model

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

$$ P_0 = 14000,\quad T_d = 10,\quad t = 8 $$

Calculate the population at t = 8

$$ P(8) = 14000 \cdot 2^{\frac{8}{10}} = 14000 \cdot 2^{0.8} $$

$$ 2^{0.8} \approx 1.741101127 $$

$$ P(8) \approx 14000 \cdot 1.741101127 \approx 24375.4158 $$

Round to the nearest whole number

$$ P(8) \approx 24375 $$

Answer:

What will the population be in 8 years?
<blank>24,375</blank>
(Round to the nearest whole number as needed.)