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) = (1.35)^t/6 +5 Complete the following sentence about the daily percent change in the mass of the sunfish. Round your answer to the nearest percent. Every day, there is a % addition to/ removal from the mass of the sunfish.​

Answer 1

The daily percent change in the mass of the ocean sunfish is approximately 5%, indicating that there is a 5% addition to its mass every day due to its exponential growth pattern.

Step-by-step explanation:

To determine the daily percent change in the mass of the ocean sunfish, we need to analyze the given function M(t) = (1.35)^t/6 + 5. This function represents exponential growth since the base of the exponent (1.35) is greater than 1. To find the daily percent change, we look at the factor by which the mass increases each day.

When t increases by 1 (representing one day), the new mass is:

M(t+1) = (1.35)^{(t+1)/6} + 5

We are interested in the ratio of M(t+1) to M(t), but since the +5 is a constant addition, it does not affect the daily percentage change. Let's calculate the growth factor for one day:

Growth Factor = (1.35)^(1/6)

To find the percent change we subtract 1 from the growth factor and then multiply by 100:

Daily Percent Change = ((1.35)^(1/6) - 1) × 100

Computing this we get an approximate value of 5.3%. So, every day, there is approximately a 5% addition to the mass of the sunfish.