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, (t), in days, since an ocean sunfish is born, and its mass, (M(t)), in milligrams, is modeled by the following function:

[ M(t) = 3 cdot (8149)^t ]

Complete the following sentence about the rate of change in the mass of the sunfish. Round your answer to two decimal places. The mass of the sunfish increases by a factor of:

a) ( 7/9 ) every (t) days.

b) ( 9/7 ) every (t) days.

c) ( 1/2 ) every (t) days.

d) ( 2/1 ) every (t) days.

Answer 1

The mass of the sunfish increases by a factor of 8149 every day.

Step-by-step explanation:

The given function for the mass of an ocean sunfish is M(t) = 3 * (8149)^t, where t represents the elapsed time in days since the sunfish is born, and M(t) represents its mass in milligrams.

To determine the rate of change in the mass of the sunfish, we need to analyze how the mass changes with each day. To do this, we can compare the mass at a given day (t+1) with the mass at the previous day (t). Taking the ratio of these two masses will give us the factor by which the mass increases:

M(t+1) / M(t) = [3 * (8149)^(t+1)] / [3 * (8149)^t]

Canceling out the common factors, we have:

M(t+1) / M(t) = (8149) / 1 = 8149.

Therefore, the mass of the sunfish increases by a factor of 8149 every day.