Answer :
To approximate the expression [tex]\( 22 e^{0.042 \times 8} \)[/tex], follow these steps:
1. Calculate the exponent:
- Multiply the base of the exponent ([tex]\(0.042\)[/tex]) by [tex]\(8\)[/tex].
- [tex]\(0.042 \times 8 = 0.336\)[/tex].
2. Use the exponential function:
- Find the value of [tex]\(e^{0.336}\)[/tex]. You can use a calculator for this step. The constant [tex]\(e\)[/tex] is approximately equal to 2.71828.
- Computing [tex]\(e^{0.336}\)[/tex] will give you an approximate value, which is about 1.399.
3. Multiply by the base number:
- Multiply the result from the exponential calculation by the base number [tex]\(22\)[/tex].
- [tex]\(22 \times 1.399 \approx 30.785\)[/tex].
4. Round the result:
- The final step is to round the result to three decimal places.
- [tex]\(30.785\)[/tex] is already rounded to three decimal places, so no further rounding is needed.
Hence, the approximation of [tex]\(22 e^{0.042 \times 8}\)[/tex] is [tex]\(30.785\)[/tex].
1. Calculate the exponent:
- Multiply the base of the exponent ([tex]\(0.042\)[/tex]) by [tex]\(8\)[/tex].
- [tex]\(0.042 \times 8 = 0.336\)[/tex].
2. Use the exponential function:
- Find the value of [tex]\(e^{0.336}\)[/tex]. You can use a calculator for this step. The constant [tex]\(e\)[/tex] is approximately equal to 2.71828.
- Computing [tex]\(e^{0.336}\)[/tex] will give you an approximate value, which is about 1.399.
3. Multiply by the base number:
- Multiply the result from the exponential calculation by the base number [tex]\(22\)[/tex].
- [tex]\(22 \times 1.399 \approx 30.785\)[/tex].
4. Round the result:
- The final step is to round the result to three decimal places.
- [tex]\(30.785\)[/tex] is already rounded to three decimal places, so no further rounding is needed.
Hence, the approximation of [tex]\(22 e^{0.042 \times 8}\)[/tex] is [tex]\(30.785\)[/tex].
