10. Biologists leamed that the shoulder height, \( h \), in centimeters, of a male African elephant can be modeled by the formula below, where \( t \) is the age in years of the elephant. \[ h=62.5 \sqrt[3]{t}+75.8 \] If the shoulder height of an elephant ( \( h \) ) is 275 centimeters, approximately how old (t) might the elephant be?

To find the age \( t \) of the elephant when its shoulder height \( h \) is 275 cm, we start with the equation provided: \[ h = 62.5 \sqrt[3]{t} + 75.8 \] Setting \( h \) to 275 cm, we will plug in the value and solve for \( t \): \[ 275 = 62.5 \sqrt[3]{t} + 75.8 \] Subtracting 75.8 from both sides gives: \[ 275 - 75.8 = 62.5 \sqrt[3]{t} \] \[ 199.2 = 62.5 \sqrt[3]{t} \] Next, we divide both sides by 62.5: \[ \sqrt[3]{t} = \frac{199.2}{62.5} \] Calculating the right side yields: \[ \sqrt[3]{t} \approx 3.1872 \] Now we will cube both sides to solve for \( t \): \[ t = (3.1872)^3 \] Calculating that gives: \[ t \approx 32.3 \] Thus, the elephant is approximately 32 years old.