Question

Urgent help!

In 1982 the number of Starbucks was 5 shops. It has exponentially grown by 21% yearly.

A: write a function (equation) that models the number of Starbucks n(t) in t years

B: find the project number of shops after 15 years

C: find the number of years required for the number of shops to reach 500

Answer 1

Answer: Check below!!!

Step-by-step explanation: A) n(t) = 5 * (1 + 0.21)^t

B) To find the projected number of shops after 15 years, we can plug in

t = 15 into the equation:

n(15) = 5 * (1 + 0.21)^15 = 5 * 2.157 = 10.785

So, after 15 years, the projected number of Starbucks would be approximately 10.785.

C) 500 = 5 * (1 + 0.21)^t

Taking the natural logarithm of both sides, we get:

ln(500) = ln(5 * (1 + 0.21)^t)

ln(100) = ln((1 + 0.21)^t)

Using logarithm properties, we can simplify the equation to:

2 = t * ln(1 + 0.21)

And finally, solving for t, we get:

t = 2 / ln(1 + 0.21)

t ≈ 40.07

So, it would take approximately 40.07 years for the number of Starbucks to reach 500.