Your grandfather likes to tell the story about how he started with 50 head of cattle on his ranch and grew the ranch to 1,000 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)18.63 years
B)31.43 years
C)25.22 years
D)47.65 years

Question

Quizplus · Accepted Answer

To find out how long it took for your grandfather to grow the ranch to 1,000 head of cattle, we can use the formula for compound interest:

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

Where:
A = final amount (1,000 head of cattle)
P = initial amount (50 head of cattle)
r = annual interest rate = 10% = 0.1
n = number of times the interest is compounded per year
t = time (in years)

We want to solve for t, so we can rearrange the formula:

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

Plugging in the values, we get:

t = (ln(1,000/50)) / (1 ln(1 + 0.1/1))
t = 31.43 years

Therefore, your grandfather took 31.43 years to grow the ranch to 1,000 head of cattle with an annual growth rate of 10%. The answer is B.

Your Grandfather Likes to Tell the Story About How He