Question

if you got:
exponential decay
l
now find:
a town with a population of 15,000 people grows at a rate of 3% per year. how many people will there be in 10 years?

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is \( P(t) = P_0(1 + r)^t \), where \( P_0 \) is the initial population, \( r \) is the growth rate (as a decimal), \( t \) is the time in years, and \( P(t) \) is the population after \( t \) years.

Step2: Plug in the given values

Here, \( P_0 = 15000 \), \( r = 0.03 \) (since 3% = 0.03), and \( t = 10 \). So we substitute these into the formula: \( P(10) = 15000(1 + 0.03)^{10} \).

Step3: Calculate \( (1 + 0.03)^{10} \)

First, calculate \( 1 + 0.03 = 1.03 \). Then, \( 1.03^{10} \approx 1.343916379 \) (using a calculator or exponentiation rules).

Step4: Multiply by the initial population

Multiply \( 15000 \) by \( 1.343916379 \): \( 15000 \times 1.343916379 \approx 20158.74569 \). Rounding to a whole number (since we can't have a fraction of a person), we get approximately 20159.

Answer:

Approximately 20159 people.