Question

Enter an exponential growth function to model each situation. Then find the value of the function after the given amount of time. Use t to represent the time in yearsRound the value for the population after the given amount of time to the nearest hundredth. The population of a small town is 1.700 and is increasing at a rate of 2% per year; 10 years.

Answer 1

Exponencial function: P = 1700 * (1 + 0.02)^t

For t = 10 years: P = 2072.29

Explanation:

The exponencial function is given by:

P = Po * (1 + r)^t

Where P is the final value, Po is the inicial value, r is the rate and t is the time.

In this case, we have that Po = 1700, r = 2% = 0.02 and t = 10 years.

So using these values in the equation, we can find the value of P:

P = 1700 * (1 + 0.02)^10

P = 1700 * (1.02)^10

P = 2072.29

So the population after 10 years will be 2072.29

Answer 2

Exponential growth function: P = 1700*e^(0.02*t)

After 10 years, the amount of population will be 2076

Explanation:

Population growth is modeled by the following equation:

P = P0*e^(r*t)

where P is final population, P0 is initial population, r is rate of growth (as decimal) and t is time (in years)

Replacing with P0 = 1700, r = 0.02 and t = 10, we get:

P = 1700*e^(0.02*10) = 2076.38