Question

Use the following function rule to find f(0.21). f(x) = 8.48 + x 0.75 Write your answer as a decimal or whole number. f(0.21) =

Answer 1

To find \( f(0.21) \) using the function rule \( f(x) = 8.48 + x^{0.75} \), we will substitute \( x = 0.21 \) into the function:

\[
f(0.21) = 8.48 + (0.21)^{0.75}
\]

Now we need to calculate \( (0.21)^{0.75} \).

1. Calculate \( 0.21^{0.75} \):
\[
0.21^{0.75} = (0.21^{3/4}) = \sqrt[4]{0.21^3}
\]
First, calculate \( 0.21^3 \):
\[
0.21^3 = 0.21 \times 0.21 \times 0.21 = 0.009261
\]
Next, calculate the fourth root of \( 0.009261 \):
\[
0.009261^{0.25} \approx 0.120388
\]

2. Substitute back into the function:
\[
f(0.21) = 8.48 + 0.120388 \approx 8.600388
\]

Rounded to three decimal places:
\[
f(0.21) \approx 8.600
\]

Thus, the final answer is:
\[
\boxed{8.60}
\]