Question

Ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish.

Answer 1

Answer:

Half (1/2)

Step-by-step explanation:

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

$M(t)=3(\frac{81}{49})^{t}$

This expression shows that the mass of sunfish increases by a factor of $\frac{81}{49}$ after each day. For example one day 1, the mass of sunfish would be:

$M(1)=3(\frac{81}{49} )$

And on day 2:

$M(2)=3(\frac{81}{49} )^{2}$

We can re-write the given equation as:

$M(t)=3(\frac{9^{2}}{7^{2}} )^{t}\\\\ M(t)=3((\frac{9}{7})^{2})^{t}\\\\ M(t)=3(\frac{9}{7})^{2t}$

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:

$M(t)=3(\frac{9}{7})^{2}$

After 1.5 day, the mass would be:

$M(t)=3(\frac{9}{7})^{1.5 \times 2}\\\\ M(t)=3(\frac{9}{7} )^{3}$

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