Question

Biologists have discovered that the shoulder height h (in centimeters) of a male African elephant can be modeled by where t is the age of the elephant in years. Estimate the height of an elephant

Answer 1

GIVEN:

We are given a function that models the shoulder height of an African Elephant as shown below;

`h(t)=62.5\sqrt[3]{t}+75.8`

T is the age of the Elephant in years.

Required:

To estimate the height of an Elephant that is 10 years old.

Step-by-step solution;

To solve this problem, we have the age of the Elephant as t in the function. Where the age is now given as 10 years, we will simply substitute for t equals 10 into the function.

We now have;

`\begin{gathered} h(t)=62.6\sqrt[3]{t}+75.8 \\ \\ Where\text{ }t=10 \\ \\ h(10)=62.5\sqrt[3]{10}+75.8 \\ \\ h(10)=(62.5*2.15443469003)+75.8 \\ \\ h(10)=134.652168127+75.8 \\ \\ h(10)=210.452168127 \end{gathered}`

We can now approximate this to the nearest whole number and we'll have;

`h(10)=210`

Therefore,

ANSWER:

For a 10 year old Elephant, the height is 210 cm.

The last option is the correct answer.