Question

The population P (in thousands) of Horry County, South Carolina from 1970 to 2007 can be modeled by P=-18.5+92.2e.0282t where t represents the year, with t =0 corresponding to 1970. a) What was the population in year 1970?

Answer 1

$\begin{gathered} P=73.7\text{ (in thousands)} \\ P=73700\text{ people} \end{gathered}$

Explanation

$P=-18.5+92.2e^{0.0282t}$

Step 1

to find the populatin in 1970,it is t=0, replace,

$\begin{gathered} P=-18.5+92.2e^{0.0282t} \\ P=-18.5+92.2e^{0.0282\cdot0} \\ P=-18.5+92.2e^0^{} \\ e^0=1 \\ P=-18.5+92.2\cdot1 \\ P=-18.5+92.2 \\ P=73.7\text{ (in thousands)} \end{gathered}$

73700 people

I hope this helps you