Question

Since 2008, the net sales S of a coffee company have grown exponentially at the rate of 46.3% per year. This growth can be modeled by dSdt=0.463S, and the function S satisfying this equation is S=500000e0.463t. How many years will it take for the net sales to double? (Round to three decimal places, and don't include units)

Answer 1

Answer:

1.497

Step-by-step explanation:

If net sales are given by the function:

$S=500,000*e^{0.463t}$

The initial net sales, at t = 0 are:

$S=500,000*e^{0.463*0}\\S=500,000$

In order for sales to double, then S(t) must be equal to 1,000,000. The time 't', in years, required for sales to double is:

$1,000,000=500,000*e^{0.463t}\\2=e^{0.463t}\\ln(2) = 0.463t\\t=1.497\ years$

It will take 1.497 years for net sales to double.

Answer 2

Answer:

1.497 years

Step-by-step explanation:

$S=500000e^{0.463t}$

In 2008, t = 0

$S=500000e^{0.463\times 0} = 500000$

When sales are doubled, S = 1000000

$1000000=500000e^{0.463t}$

$e^{0.463t} = 2$

$0.463t = \ln 2 = 0.693$

$t = \dfrac{0.693}{0.463} = 1.497$

Therefore, sales will double in 1.497 years