Question

Karina has determined that the weight of a newborn elephant increases at a rate of 6% per week for the first 14 weeks. She

needs to determine how much weight a baby elephant will gain on the 14th week if it weighs 92 lbs. at birth. Write the explicit
formula of the geometric sequence that could be used to model this scenario.

Answer 1

Answer: W(n) = 92lb*1.06^n

and W(14) = 92lb*1.06^14 = 208lb

Explanation:

We know that at the beginning the baby elephant weighs 92Lbs, and for each week it augments by a 6% (or 0.06 in decimals)

Then, at the end of the first week, the weight is:

92lb*1.06 = 97.52lb

at the end of the second week:

(92lb*1.06)*1.06 = 103.37lb

and so on, so you can see that the pattern is:

W(n) = 92lb*1.06^n

where n is the number of weeks after the birth

W(0) = 92lb

W(1) = 97.52lb

...

And we want to know the weight at the end of the 14th week, so we must find:

W(14) = 92lb*1.06^14 = 208lb

Answer 2

This is an exponential growth problem.

The formula is y = a(1+r)^x

Y would be the final answer

a is the starting value

r is the percent of growth

x is the amount of time ( number of weeks)

The equation is:

y(x) = 92(1.06)^x

For 14 weeks replace x with 14:

y(14) = 92(1.06)^14 = 208 pounds.