how do you find the ratio in years! in this Question?

Question

the average weight w(in pounds) of an atlatic cod can be modeled by where t is the age of the fish( in years). Find the ratio ofthe weight of 5-year-old cod to the weight of a 2-year-old cod.

the equation is w=1.21(1.420)^t

Answer 1

Start with your equation: w=1.21(1.420)^t

Rather than plug in both numbers at first, instead, write up a fraction with both ages:

ratio = 1.21(1.420)^5 / 1.21(1.420)^2

Notice what cancels: the 1.21 cancels, and (1.420)^5/(1.420)^2 cancels to become (1.420)^3.

That's your ratio:
(1.420)^3:1
2.863:1