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 2019 in billions of dollars.
$
billion

(b) Use the model to estimate the sales in 2023 in billions of dollars.
$
billion

Answer 1

To estimate the sales in 2019, we need to find the value of S(t) when t = 19, since t = 9 corresponds to 2009. We can plug in t = 19 into the given function and simplify:

S(19)=3.71(1.112)^19

S(19)≈18.77

Therefore, the estimated sales in 2019 are $18.77 billion.
(b) To estimate the sales in 2023, we need to find the value of S(t) when t = 23, since t = 9 corresponds to 2009. We can plug in t = 23 into the given function and simplify:

S(23)=3.71(1.112)^23

S(23)≈28.64

The estimated sales in 2023 are $28.64 billion.