Chapter 3, Problem 1RE

Use a calculator to evaluate A = 2,000e^0.09t to the nearest cent for t = 5, 10, and 20.

To determine

To evaluate: The equation $A=2,000e^{0.09t}$ for $t=5,10\text{and 2}0$ by using the calculator.

Answer to Problem 1RE

The values for the variable is $A=3,136.62,4,919.21\text{and}12,099.29$.

Explanation of Solution

The given variable is $A=2,000e^{0.09t}$.

Use a calculator to evaluate A for t = 5 as follows,

$\begin{array}{c}A=2,000e^{0.09\left(5\right)}\\ =2,000e^{0.45}\\ =2,000\left(1.56831\right)\\ \approx 3,136.62\end{array}$

Use a calculator to evaluate A for t = 10 as follows,

$\begin{array}{c}A=2,000e^{0.09\left(10\right)}\\ =2,000e^{0.9}\\ =2,000\left(2.459603\right)\\ \approx 4,919.21\end{array}$

Use a calculator to evaluate A for t = 20 as follows,

$\begin{array}{c}A=2,000e^{0.09\left(20\right)}\\ =2,000e^{1.8}\\ \approx 12,099.29\end{array}$

Therefore, the values of A for t = 5, 10, and 20 is $3,136.62,4,919.21\text{and}12,099.29$ respectively.