Question

A farmer raises sheep. The number of sheep in his flock changes from year to year. The number can be represented by the equation S=24(1.05)t where S is the total number of sheep in his flock and t is the number of years since he first started raising sheep. Which statement best explains the change in the number of sheep?

Answer 1

It increases by 5% each year

Explanation:

The function, S=24(1.05)t, models change in the Number of sheep over time, t.

The function represents an exponential growth model:

The function could be rewritten in the general form ;

y = Ab^x

y = number of comocafter t years

b = increase in initial amount ; b = (1 + x)

Comparing the function :

b = 1.05

b = 1 + r ; where r = rate

1.05 = 1 + r

r = 1.05 - 1

r = 0.05 = (0.05 * 100%). = 5%

It increases by 5% each year