Question

A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week. About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth of a pound.

Answer 1

Weight after 4 weeks is 0.229 pound

Solution:

Given that young channel catfish weighs about 0.1 pound

During the next 8 weeks, its weight increases by about 23% each week

So the exponential growth function is given as:

Exponential functions are given by

$y = a(1+r)^x$

where a is the initial amount, r is the rate of growth, and x is the amount of time and y is the weight after "x" weeks

In our case, a = 0.1, r = 0.23 ( that is 23 % ) and t = 4

Thus we get,

$y = 0.1(1 + 0.23)^4$

$y = 0.1(1.23)^4\\\\y = 0.1 \times 2.289\\\\y = 0.229$

Thus weight after 4 weeks is 0.229 pound