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*(81/49)^t

The mass of the sunfish increases by a factor of 9/7 every _______ days.

Answer 1

0.5

Explanation:

Trust me

Answer 2

Half (1/2)

Explanation:

The relation between the Mass, M(t), of the ocean sunfish and time t, in days, since it is born is given as:

`M(t)=3((81)/(49))^(t)`

This expression shows that the mass of sunfish increases by a factor of
`(81)/(49)` after each day. For example one day 1, the mass of sunfish would be:

`M(1)=3((81)/(49) )`

And on day 2:

`M(2)=3((81)/(49) )^(2)`

We can re-write the given equation as:

`M(t)=3((9^(2))/(7^(2)) )^(t)\\\\ M(t)=3(((9)/(7))^(2))^(t)\\\\ M(t)=3((9)/(7))^(2t)\\`

The exponent has changed from t to 2t. The term "2t" means 2 times in a unit time t. So this means, the mass of sunfish increases by a factor of 9/7 every 1/2(half) day.

On Day 1, the mass would be:

`M(t)=3((9)/(7))^(2)`

After 1.5 day, the mass would be:

`M(t)=3((9)/(7))^(1.5 * 2)\\\\ M(t)=3((9)/(7) )^(3)`

This example shows that the mass of sunfish increases by a factor of 9/7 after every half of the day.