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Question 10 of 10

For the function [tex]f(t) = P e^{rt}[/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. 940.0
B. 9.4
C. 0.1
D. 11.4


Sagot :

To solve for the function [tex]\( f(t) = P e^{r t} \)[/tex], given [tex]\( P = 7 \)[/tex] and [tex]\( r = 0.07 \)[/tex], we need to determine the value of [tex]\( f(7) \)[/tex] to the nearest tenth.

Let's break it down step by step:

1. Identify the given values:
- [tex]\( P = 7 \)[/tex]
- [tex]\( r = 0.07 \)[/tex]
- [tex]\( t = 7 \)[/tex]

2. Substitute the values into the function [tex]\( f(t) = P e^{r t} \)[/tex]:
[tex]\[ f(7) = 7 \cdot e^{0.07 \cdot 7} \][/tex]

3. Calculate the exponent [tex]\( 0.07 \cdot 7 \)[/tex]:
[tex]\[ 0.07 \cdot 7 = 0.49 \][/tex]

4. Find the value of [tex]\( e^{0.49} \)[/tex]:
We know the base of the natural logarithm, [tex]\( e \)[/tex], is approximately 2.71828. Evaluating [tex]\( e^{0.49} \)[/tex]:
[tex]\[ e^{0.49} \approx 1.63231 \][/tex]

5. Multiply this result by 7:
[tex]\[ 7 \cdot 1.63231 \approx 11.426213539687653 \][/tex]

6. Round this value to the nearest tenth:
[tex]\[ 11.426213539687653 \approx 11.4 \][/tex]

Therefore, the value of [tex]\( f(7) \)[/tex] to the nearest tenth is [tex]\( 11.4 \)[/tex].

The correct answer is:
D. 11.4