Approximate the following number using a calculator.
(Round to three decimal places as needed.)

Ask by Wagner Cox. in the United States

Mar 26,2025

Question

Approximate the following number using a calculator. $$ 7.9\left(\frac{1}{5}\right)^{2.2} $$ $$ 7.9\left(\frac{1}{5}\right)^{2.2} \approx \square $$ (Round to three decimal places as needed.)

UpStudy AI · Accepted Answer

We start with the expression:
$$
7.9\left(\frac{1}{5}\right)^{2.2}
$$

First, rewrite $$\left(\frac{1}{5}\right)^{2.2}$$ as:
$$
\left(\frac{1}{5}\right)^{2.2} = 5^{-2.2}
$$

Express $$5^{-2.2}$$ using the exponential function:
$$
5^{-2.2} = e^{-2.2 \ln 5}
$$

Using a calculator, compute the exponent:
$$
-2.2 \ln 5 \approx -2.2 \times 1.6094 \approx -3.54068
$$

Then, evaluate the exponential:
$$
e^{-3.54068} \approx 0.0288
$$

Now, multiply by $$7.9$$:
$$
7.9 \times 0.0288 \approx 0.2275
$$

Rounding to three decimal places gives:
$$
0.2275 \approx 0.228
$$

Thus, the final approximation is:
$$
7.9\left(\frac{1}{5}\right)^{2.2} \approx 0.228
$$
$$7.9\left(\frac{1}{5}\right)^{2.2} \approx 0.228$$

Approximate the following number using a calculator.
(Round to three decimal places as needed.)

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