Exponential decay

Question

A share of ABC stock was were $60 into thousand and five and is only worth $45 in 2010 find the multiplier and the percent decrease

Answer 1

Hi, it appears that the following is what you were trying to communicate.

Price: $60 in 2005

Price: $45 in 2010

Using the initial information, we have A = 60(1 + r)^t where P (principal) = 60, r = rate, and t = time

Using the second piece of information, we can begin to solve that equation:

45 = 60(1 + r)⁵ Observe that t = 5 because 5 years have elapsed from 2005 to 2010.

We are now going to solve for r.

Divide both sides by 60

3/4 = (1 + r)⁵

Now, take the 5th root on both sides

3^1/5/4^1/5 = 1 + 4

Solve the left hand side using a calculator (rounding is required)

0.9441 ≈ 1 + r

Subtract 1 from both sides to get r

r ≈ -0.0558

Answer #1: This means that the multiplier (1 + r) is roughly ≈0.9441 or 94.41%

Answer #2: r ≈ -0.0558 so the percent decrease is roughly 5.58%