The number of years that a stock of $40 increases to $50 at a rate of 8% per year can be written by the logarithmic expression:
log1.08(50 over 40)
a. use your calculator to determine how many years it will take for the stock to reach $50.
50 = 40(1.08)^n
50/40 = 1.08^n
n log 1.08 = log(5/4)
n = log(5/4) / log 1.08
= 2.899 or appr 2.9 years
check:
40(1.08)^2.9 = 50.002
Your expression is incorrect
To use the logarithmic expression log1.08(50/40), you can follow these steps:
1. Divide 50 by 40 to find the ratio: 50 / 40 = 1.25
2. Take the logarithm of the ratio using the base 1.08. You can do this by using a calculator with logarithmic functions.
Plugging the expression log1.08(1.25) into a calculator will give you the answer.
The result of this calculation is approximately 0.028593. This means that log1.08(1.25) is approximately 0.028593.
So, it will take approximately 0.028593 years for the stock to reach $50.