To estimate the height of a male African elephant that is 2 years old using the given formula, we will follow the steps below:
1. Identify the given formula: The shoulder height [tex]\( h(t) \)[/tex] in centimeters is given by the formula
[tex]\[
h(t) = 62.5 \sqrt{t} + 75.8
\][/tex]
2. Substitute the age [tex]\( t \)[/tex] into the formula: Here, [tex]\( t \)[/tex] is given as 2 years. So, we need to substitute [tex]\( t = 2 \)[/tex] into the formula.
[tex]\[
h(2) = 62.5 \sqrt{2} + 75.8
\][/tex]
3. Calculate the value of [tex]\( \sqrt{2} \)[/tex]: Using the square root function, we find that [tex]\( \sqrt{2} \approx 1.414 \)[/tex].
4. Multiply 62.5 by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[
62.5 \times 1.414 \approx 88.375
\][/tex]
5. Add this value to 75.8 to get the total height:
[tex]\[
h(2) \approx 88.375 + 75.8 = 164.175
\][/tex]
6. Compare the calculated height to the provided options: According to the calculations, the height we found is approximately 164.175 cm. Looking at the given options again:
- 270 cm
- 325 cm
- [tex]\( \pi 8 \)[/tex]
- 245 cm
None of these options match our calculation closely, but the actual numerical result from our detailed solution is approximately 164.18 cm.
