The annual revenue of Amazon.com rose from approximately $10.7 billion in 2006 to $34.2 billion in 2010. A) Find an exponential model for Amazon.com's annual revenue as a function of time t in years since 2000. Keep 8 decimal places when doing computations, but round the numbers in your model to 2 decimal places. B) What annual revenue does the model predict Amazon.com will have in 2015? C) By what percentage is the revenue increasing each year?
Added by Luis Miguel V.
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com's annual revenue as a function of time t in years since 2000. Given: Annual revenue in 2006 (t=6): $10.7 billion Annual revenue in 2010 (t=10): $34.2 billion The exponential function is given by: \( y = a \cdot b^{2x} \) Substitute the values for t=6 and Show more…
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Amazon's revenue was growing at the rate of $$ R^{\prime}(t)=0.545043 e^{0.291 t} \quad(0 \leq t \leq 6) $$ billion dollars/year in year $t$ with $t=0$ corresponding to $2006 .$ The revenue of the company for 2006 was $\ 10.71$ billion. a. By how much did the revenue of Amazon increase over the period from 2006 through $2012 ?$ b. What was the revenue of the company in $2012 ?$
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The annual revenue of Amazon.com rose from approximately $10.7 billion in 2006 to $34.2 billion in 2010. (a) Use this information to find both a linear model and an exponential model for Amazon.com's annual revenue (I) in billions of dollars as a function of time (t) in years since 2000. HINT [See Example 2.] (Round all coefficients to three significant digits.) linear model: I(t) = exponential model: I(t) = Which of these models would you judge to be more appropriate to the data shown below? t (Year since 2000) 6 7 8 9 10 I ($ billions) 10.7 14.8 19.2 24.5 34.2 The ---Select--- linear model exponential model is more appropriate. (b) Use the better of the two models from part (a) to predict the 2007 figure and compare it with the actual figure above. (Round your answer to one decimal place.) The model yields an estimate of $ billion, which is not too far from the actual figure.
Carson M.
Since 2013, the annual revenue earned by Amazon can be modeled by R(x) = 1.2x^2 + 11.62x + 62.22, where x is the number of years since 2013 and R(x) is the annual revenue in billions of dollars. To find the difference in revenue between the fourth year and the first year, we can use the formula (R(4) - R(1))/(4 - 1).
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