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The revenue of Apple® went from $54.5 billion in 2013 to $74.6 billion1 in 2015. Find an exponential function to model the revenue as a function of years since 2013. What is the continuous percent growth rate, per year, of revenue?

(I have the percent rate, I need the exponential equation in Ae^kt form! )

Respuesta :

r = continuous growth rate

revenue t years after 2013 = 54.5×10⁹×e^(rt)

74.6×10⁹ = 54.5×10⁹×e^(2r)

e^(2r) = 74.6/54.5

2r = ln(74.6/54.5)

r = ½ln(74.6/54.5) ≅ 0.15697 = 15.697% per year

Hope this helps!

fichoh

The continous percentage growth rate is 15.7%

General form of an exponential function : Ae^kt

A = original price

k = growth rate

Revenue since year 2013 :

A = revenue in year 2013

t = 2015 - 2013 = 2 years

The function becomes :

Revenue in 2015 = (Revenue in 2013)e^2k

Solve for k

74,600,000,000 = 54,500,000,000e^2k

Isolate e^2k

74,600,000,000 / 54,500,000,000 = e^2k

1.3688073 = e^2k

Take the In of both sides :

In(1.3688073) = 2k

0.3139398 = 2k

Divide both sides by 2

0.3139398/2 = k

k = 0.15696 = 0.157

0.157 × 100% = 15.7%

Learn more : https://brainly.com/question/3127939?referrer=searchResults

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