Your grandfather likes to tell the story about how he started his ranch with 100 head of cattle and grew the ranch to 2,500 head of cattle.He said "My plan was simple: grow the number of head of cattle at a rate of 10% per year." Your grandfather reached his goal before he retired.How long did it take him?
A)38.63 years
B)33.77 years
C)31.43 years
D)27.65 years

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = final amount
P = principal amount (the initial number of head of cattle)
r = annual interest rate (in this case, 10%)
n = number of times the interest is compounded per year (assuming annual compounding, n = 1)
t = time in years

We are trying to find t, so we can rearrange the formula to solve for t:

t = (ln(A/P))/(n * ln(1 + r/n))

Plugging in the numbers from the problem, we get:

t = (ln(2500/100))/(1 * ln(1 + 0.1/1))
t = (ln(25))/(ln(1.1))
t = 31.43 years (rounded to two decimal places)

Therefore, the answer is C) 31.43 years.

Your Grandfather Likes to Tell the Story About How He