a company gives its employees a 4% raise at the beginning of every year.This year Jordan earns 32000.
Could you plz tell me how I get the year at which he earns,$40000?
You are looking at a GS with
a = 32000
r = 1.04
term(n) = a r^(-1)
term(n) = 32000(1.04)^(n-1)
32000(1.04)^(n-1) = 40000
1.04^(n-1) = 1.25
take logs of both sides and use log rules
(n-1)log1.04 = log1.25
n-1 = log1.25/log1.04 = 5.689
n = 6.689
The question does not say when the change in salary takes place. I would assume at the the beginning of a new year.
thank you
To find the year in which Jordan earns $40,000, we can use the concept of compound interest. In this case, the raise of 4% per year acts as the interest rate. We can solve this problem by setting up an equation and solving for the number of years it takes for Jordan's salary to reach $40,000.
Let's use the following variables:
- C: Jordan's current salary
- r: Annual raise rate as a decimal (in this case, 4% is equivalent to 0.04)
- n: Number of years
- A: Salary after n years (in this case, $40,000)
Using the compound interest formula for exponential growth, we have:
A = C(1 + r)^n
We can plug in the values we know:
32000(1 + 0.04)^n = 40000
To solve for n, we need to isolate it. Let's divide both sides of the equation by 32000:
(1 + 0.04)^n = 40000 / 32000
Simplifying further:
(1.04)^n = 1.25
To solve for n, we can take the logarithm of both sides with base 1.04:
log base 1.04 (1.04)^n = log base 1.04 1.25
This simplifies to:
n = log base 1.04 1.25
Using a calculator, we can find the approximate value of n to determine the year at which Jordan earns $40,000.