Question

a marine biologist uses a linear model to estimate the weight of a blue whale after it is born. the model estimated that a certain blue whale weighs 5,710 pounds at birth and gains 10.0 pounds per hour for 120 hours, after it is born. based on this model, what is the estimated weight, in pounds, of this blue whale 7 hours after it is born?

Explanation:

Step1: Identify the linear - model formula

The linear - model for weight $w$ as a function of time $t$ (in hours) is $w=w_0 + rt$, where $w_0$ is the initial weight, $r$ is the rate of weight - gain per hour, and $t$ is the time in hours. Given $w_0 = 5710$ pounds and $r = 10$ pounds per hour.

Step2: Substitute the values into the formula

We want to find the weight $w$ when $t = 120$ hours. Substitute $w_0=5710$, $r = 10$, and $t = 120$ into the formula $w=w_0+rt$. So $w=5710+10\times120$.

Step3: Calculate the result

First, calculate $10\times120 = 1200$. Then, $w=5710 + 1200=6910$ pounds.

Answer:

6910 pounds