Question

Ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish. The relationship between the elapsed time, ttt, in days, since an ocean sunfish is born, and its mass, M_{\text{day}}(t)M day ​ (t)M, start subscript, start text, d, a, y, end text, end subscript, left parenthesis, t, right parenthesis, in milligrams, is modeled by the following function: Mday(t)=3.5⋅(1.05)t Complete the following sentence about the weekly rate of change in the mass of the sunfish. Round your answer to two decimal places. Every week, the mass of the sunfish increases by a factor of .

Answer 1

1.4071

Explanation:

The relationship between the elapsed time, t in days, since an ocean sunfish is born, and its mass is given by:

`M_(day)(t)=3.5(1.05)^t`

This function represents an exponential growth increasing as the number of days increases since (3.5 > 1), it means that at day 0 , the mass of the sunfish is 3.5 milligrams and every day, its mass increases by a factor of 1.05.

Since the mass of the sunfish increases by
`1.05^t`, therefore the mass of the sunfish increases every one week (that is 7 days) by a factor of
`1.05^(7) = 1.4071`