Question

The sales S (in billions of dollars) for Starbucks from 2009 through 2014 can be modeled by the exponential function
S(t) = 3.71(1.112)t
where t is the time in years, with
t = 9
corresponding to 2009.† (Round your answers to two decimal places.)
(a) Use the model to estimate the sales in 2017 in billions of dollars.
$

Incorrect: Your answer is incorrect.
billion

(b) Use the model to estimate the sales in 2024 in billions of dollars.
$

Incorrect: Your answer is incorrect.
billion

Answer 1

Step-by-step explanation:

S(t) = 3.71(1.112)^t

means simply :

in the year 2000 they had sales of 3.71 billion dollars.

and every year their sales goes up by 11.2% (the sales of the previous year is multiplied by 1.112).

so, their sales was in 2009 (t = 9)

S(9) = 3.71(1.112)⁹ = 9.645327865...

≈ 9.65 billion dollars.

(a)

in 2017 (t = 17) their sales was then

S(17) = 3.71(1.112)¹⁷ = 22.55045416...

≈ 22.55 billion dollars.

(b)

in 2024 (t = 24) their sales was then

S(24) = 3.71(1.112)²⁴ = 47.41205762...

≈ 47.41 billion dollars.