Question

The population P of a city is given by P = 115600e^0.024t, where t is the time in years. According to this model, after how many years will the population be 130,000?4.29 years4.89 years5.19 years4.49 years

Answer 1

Given:

The population P of a city is given by,

`P=115600e^(0.024t,)`

To find:

The time taken for the population to reach 130,000.

Step-by-step explanation:

Substituting P = 130,000 in the given function, we get

`\begin{gathered} 130000=115600 \\ e^(0.024t)=(130000)/(115600) \\ e^(0.024t)=1.1245 \\ 0.024t=\ln1.1245 \\ 0.024t=0.1174 \\ t=4.891 \\ t\approx4.89years \end{gathered}`

Therefore, the number of years required for the population to reach 130,000 is 4.89years.

Final answer:

The number of years required is 4.89years.