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(t)M(t)M, left parenthesis, t, right parenthesis, in milligrams, is modeled by the following function:
M(t)=(1.35)t6+5

Answer 1

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

In this function:

M(t) represents the mass of the ocean sunfish in milligrams at time t days.

t is the elapsed time in days since the ocean sunfish is born.

The function uses an exponential term (t^6) to model the rapid growth in mass over time. The constant 1.35 determines how fast the mass increases, and the constant 5 represents an initial mass, possibly at birth or at some reference time.

As time (t) increases, the mass of the ocean sunfish (M(t)) will grow rapidly, with the rate of growth determined by the value of t^6 and the scaling factor of 1.35.