After 14 months after the first month would the sales reach $9000
For given question,
A Hammer Hardware has sales of $5000 in its first month.
The sales were to increase by 4% every month.
We need to find the number of months after the first month would the sales reach $9000
Let the exponential function for sales is,
f(n)= a (1 + r)^{n}
where, n is the number of months
a is the sales of the first month
r is the rate of increment
So, a = $5000, r = 0.04, f(n) = $9000
Substitute values in above equation.
⇒ 9000 = 5000 × (1 + 0.04)^{n}
Solve above equation for n.
⇒ 1.8 = (1.04)^n
⇒ n =
⇒ n = 14.9
⇒ n ≈ 15
Therefore, after 14 months after the first month would the sales reach $9000
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