Question

A population numbers 19,000 organisms initially and grows by 4.8% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P =aâb^t where p =_________

Answer 1

Answer:

The exponential model for the population is $P(t) = 19000e^{0.048t}$

Step-by-step explanation:

The exponential model for the population has the following format:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial population and r is the growth rate, as a decimal.

A population numbers 19,000 organisms initially and grows by 4.8% each year.

This means that $P(0) = 19000, r = 0.048$

So

$P(t) = P(0)e^{rt}$

$P(t) = 19000e^{0.048t}$

The exponential model for the population is $P(t) = 19000e^{0.048t}$