Question

The sales S (in billions of dollars) for Starbucks from 2009 through 2014 can be modeled by the exponential functionS(t) = 3.71(1.112)twhere 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 2015 in billions of dollars.b) Use the model to estimate the sales in 2024 in billions of dollars.

Answer 1

`S(t)=3.71(1.112)\placeholder{⬚}^t`

a) Use the model to estimate the sales in 2015 in billions of dollars

Evaluate the function for t=15

`\begin{gathered} S(15)=3.71(1.112)\placeholder{⬚}^(15) \\ \\ S(15)\approx18.24 \end{gathered}`

The sales in 2015 will be $18.24 billion

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

Evaluate the function for t=24

`\begin{gathered} S(24)=3.71(1.112)\placeholder{⬚}^(24) \\ \\ S(24)=47.41 \end{gathered}`

The sales in 2024 will be $47.41 billion