Question

Biologists have discovered that the shoulder height h (in centimeters) of a male Asian elephant can be modeled by h=62.5 to the power of three square root t +75.8, where it is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 250 centimeters. Round your answer to the nearest 10th.

Answer 1

21.7 years

Explanation:

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

h = 250 centimeters.

`250=62.5\sqrt[3]{t} +75.8`

Subtract 75.8 on both sides to isolate the cubed root.

`174.2=62.5\sqrt[3]{t}`

Divide both sides by 62.5. 62.5 will cancel out.

`(174.2)/(62.5) =\frac{62.5\sqrt[3]{t} }{62.5}`

`2.7872 = \sqrt[3]{t}`

Square both sides by three to cancel the cube root.

`(2.7872)^(3) =(\sqrt[3]{t})^(3)`

`21.6523=t`

Round to the nearest tenth.

`t=21.7`