For the function [tex]f(t) = Pe^t[/tex], if [tex]P = 7[/tex] and [tex]r = 0.07[/tex], then what is the value of [tex]f(7)[/tex] to the nearest tenth?

A. 9.4
B. 11.4
C. 940.0
D. 0.1



Answer :

To find the value of [tex]\(f(7)\)[/tex] for the function [tex]\( f(t) = P e^{r t} \)[/tex] when [tex]\( P = 7 \)[/tex] and [tex]\( r = 0.07 \)[/tex], let's follow these steps:

1. Substitute the given values into the function:
[tex]\[ f(t) = 7 \cdot e^{0.07 t} \][/tex]
We need to find [tex]\( f(7) \)[/tex]:
[tex]\[ f(7) = 7 \cdot e^{0.07 \cdot 7} \][/tex]

2. Calculate the exponent:
[tex]\[ 0.07 \cdot 7 = 0.49 \][/tex]
So the function becomes:
[tex]\[ f(7) = 7 \cdot e^{0.49} \][/tex]

3. Evaluate the exponential term [tex]\( e^{0.49} \)[/tex]:
The value of [tex]\( e^{0.49} \)[/tex] is approximately 1.64971.

4. Multiply the result by 7:
[tex]\[ f(7) = 7 \cdot 1.64971 \approx 11.426213539687653 \][/tex]

5. Round the result to the nearest tenth:
The value [tex]\( 11.426213539687653 \)[/tex] rounded to the nearest tenth is 11.4.

So, the value of [tex]\( f(7) \)[/tex] to the nearest tenth is:
[tex]\[ \boxed{11.4} \][/tex]