Question

The population of a town was 500 in 2010. The population grows at a rate of 9.6% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010.

Answer 1

To estimate the population t years after 2010 for a town with a starting population of 500 and an annual growth rate of 9.6%, we use the exponential growth model P(t) = 500 * e^(0.096t).

Step-by-step explanation:

To calculate the population of a town with an initial population of 500 in 2010 that grows at a rate of 9.6% annually, we can use the exponential growth model. The model's equation is:

P(t) = P0 * e^(rt)

Where:

• P(t) is the population after t years
• P0 is the initial population
• e is the base of the natural logarithms (approximately 2.71828)
• r is the annual growth rate (in decimal form)

For this town:

• P0 = 500
• r = 9.6% or 0.096

Plugging these values into the equation, we get:

P(t) = 500 * e^(0.096t)

This equation will give us the estimated population of the town t years after 2010.