Question

f(x) = (1.84)^{\tfrac{x}{4}}

The function f is defined by the given equation. The equation can be rewritten as f(x) = (1 + p/100)^x where p is a constant. Which of the following is closest to the value of p?

• A. 16
• B. 21
• C. 46
• D. 96

Answer 1

Answer: (A)

16

Answer 2

We rewrite the base as a power of x:

$$f(x) = (1.84)^{\tfrac{x}{4}} = \bigl((1.84)^{1/4}\bigr)^x = \bigl(1 + \tfrac{p}{100}\bigr)^x.$$

So we need

$$1 + \frac{p}{100} = (1.84)^{1/4}.$$

Compute

$$(1.84)^{1/4} = e^{\tfrac{1}{4}\ln(1.84)} \approx e^{0.1523} \approx 1.1645.$$

Thus

$$\frac{p}{100} \approx 0.1645 \quad\Rightarrow\quad p \approx 16.45.$$

The closest option is 16.