Question

Please help me with the 2nd part!! I'm stuck on it

Answer 1

Answer:

• Country 3

,

• 2.2%

Explanation:

Given the growth rates of the four countries below:

$\begin{gathered} Country1\colon A=1262e^{0.003t} \\ Country2\colon A=141.6e^{-0.007t} \\ Country3\colon A=27.9e^{0.022t} \\ Country4\colon A=1081.5e^{0.013t} \end{gathered}$

Part A

The country with the highest growth rate is Country 3.

Part B

The equation for country 3 is given by:

$Country3\colon A=27.9e^{0.022t}$

Evaluate the exponent term:

$e^{0.022t}=1.022243^t$

We can rewrite the result further:

$1.022243^t=(1+0.022243)^t=(1+\frac{2.2243}{100})^t\approx(1+\frac{2.2}{100})^t$

The population of the country is increasing by 2.2% each year.