College

The function [tex]f[/tex] is defined by the given equation. The equation can be rewritten as [tex]f(x) = \left(1 + \frac{p}{100}\right)^x[/tex], where [tex]p[/tex] is a constant. Which of the following is closest to the value of [tex]p[/tex]?

A. 16
B. 21
C. 46
D. 96

Answer :

We are given that the function can be expressed as
[tex]$$
f(x) = \left(1 + \frac{p}{100}\right)^x.
$$[/tex]
If we observe that the equivalent expression is written with a base of approximately [tex]$1.21$[/tex], we can set up the following equation:
[tex]$$
1 + \frac{p}{100} = 1.21.
$$[/tex]

Subtracting [tex]$1$[/tex] from both sides, we get:
[tex]$$
\frac{p}{100} = 1.21 - 1 = 0.21.
$$[/tex]

Multiplying both sides by [tex]$100$[/tex] to solve for [tex]$p$[/tex], we obtain:
[tex]$$
p = 0.21 \times 100 = 21.
$$[/tex]

Thus, the value of [tex]$p$[/tex] is [tex]$21$[/tex], which corresponds to answer choice (B).

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