this is the question

Question

 

A baby catfish weights about 0.1 pound. During the next 8 weeks, its weight increases at a rate of about 27% per week.

a) Write an exponential growth function that represents the weight of the catfish 't' after t weeks during this period.

b) About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth

Answer 1

Hello, Favour,

The catfish gains 27% per week, so it's weight would be the previous week's weight times (1+0.27). The 1 keeps the previous week's weight and the 0.27 addson the 27% weight gain for that week. We keep doing this for each week. That would mean the following progression:

Week Weight Formula

0 0.1 0.1 Birth/initial weight

1 0.127 0.1(1+0.27)

2 0.161 0.1(1+0.27)*(1+0.27)

3 0.2048 0.1(1+0.27)*(1+0.27)*(1.027)

4 0.3304 0.1(1+0.27)*(1+0.27)*(1+0.27)*(1.027)*(1.027)

4 weeks rounded to the nearest thousandth would be 0.330.

You can see from the sequence of equations that a general equation for calculating wieght would be to take the initial weight and mutiply it by the quantity (1+0.27) t times, where is the number of weeks from the initial weight.

Weight = Initial*(1+0.27)^t

Bob