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_("day ")(t), in milligrams, is modeled by the following function: M_("day ")(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

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_("day ")(t), in milligrams, is modeled by the following function:  M_("day ")(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

Bytelearn · Accepted Answer

Identify Function Given: The function given is M_(＂day ＂)(t) = 3.5 * (1.05)^t, which models the mass of the sunfish in milligrams as a function of time in days. To find the weekly rate of change, we need to calculate the factor by which the mass increases every 7 days, since a week consists of 7 days.Calculate Factor After One Week: We substitute t with 7 to find the factor by which the mass increases after one week: M_(＂day ＂)(7) = 3.5 * (1.05)^7.Compute Weekly Multiplication Factor: Using a calculator, we compute (1.05)^7 to find the weekly multiplication factor. (1.05)^7 ≈ 1.40710.Round Result to Two Decimal Places: We round the result to two decimal places as instructed: 1.40710 ≈ 1.41.

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