You might need: Calculator Ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish. The relationship between the elapsed time, $t$, in days, since an ocean sunfish is born, and its mass, $M_{\text {day }}(t)$, in milligrams, is modeled by the following function: \[ M_{\text {day }}(t)=3.5 \cdot(1.05)^{t} \] 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

Step 1 ：The question is asking for the weekly rate of change in the mass of the sunfish. This means we need to find the factor by which the mass increases every week.

Step 2 ：Since the time, \( t \), is given in days, we need to convert a week into days. A week is 7 days.

Step 3 ：So, we need to substitute \( t=7 \) into the given function and find the value. This will give us the mass of the sunfish after a week.

Step 4 ：Since the mass of the sunfish at birth (t=0) is 3.5 milligrams, the weekly rate of change will be the ratio of the mass after a week to the initial mass.

Step 5 ：Let's calculate the mass of the sunfish after a week, \( M_{1} = 3.5 \cdot (1.05)^{7} \approx 4.92 \) milligrams.

Step 6 ：Then, calculate the weekly rate of change, \( \text{rate} = \frac{M_{1}}{M_{0}} \approx 1.41 \).

Step 7 ：The weekly rate of change in the mass of the sunfish is approximately 1.41. This means that every week, the mass of the sunfish increases by a factor of 1.41.

Step 8 ：Final Answer: \(\boxed{1.41}\)