Question

the threshold weight t for a person is the weight above which the risk of death increases greatly. one researcher found that the threshold weight in pounds for men aged 40 - 49 is related to height in inches by the equation h = 12.3t^{1/3}. what height corresponds to a threshold of 257 pounds for a man in this age group? what does the value of 257 represent in the given equation? t 12.3t^{1/3} t^{1/3} h the height that corresponds to 257 pounds for a man in the specified age group is (round to the nearest tenth as needed)

Explanation:

Step1: Identify the value of T

We are given that $T = 257$ pounds.

Step2: Calculate $T^{1/3}$

$T^{1/3}=257^{1/3}=\sqrt[3]{257}\approx6.36$.

Step3: Calculate the height h

Substitute $T^{1/3}$ into the formula $h = 12.3T^{1/3}$. So $h=12.3\times6.36 = 78.228$.

Step4: Round the result

Rounding $78.228$ to the nearest tenth gives $h\approx78.2$.

Answer:

$78.2$