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The weekly revenue of a business selling gummy bear bags is a continuous function of price....

Question:

The weekly revenue of a business selling gummy bear bags is a continuous function of price. Weekly revenue is $8,115 when the price per is $1.60 and the growth rate is 8%. Revenue is changing exponentially.

What will revenue be when the price is $4.60?

How fast revenue be changing when the price is $4.60?

Continuous function

A function, if plotted on a graph, forms an unbreakable curve within an interval, is called a continuous function. Mathematically, continuity of a function can be derived for an interval.

Answer and Explanation:

Given

Revenue of company is a function of price and is continuous.

Weekly revenue is{eq}$8115 {/eq}

Growth rate is 8%

Price is {eq}$1.60 {/eq}

If revenue is changing exponentially then it will be expressed as,

{eq}\begin{align*} = \dfrac{{8115}}{{1.60}}\\ = 5071 \end{align*} {/eq}

We have to calculate for price of {eq}\ $4.60 {/eq}

Thus, new weekly revenue will be,

{eq}4.60 \times 5071 =$ 23326 {/eq}

Therefore, change in revenue rate,

{eq}\begin{align*} &\left[ {\dfrac{{{\rm{new weekly revenue}}}}{{{\rm{previous weekly revenue}}}} - 1} \right] \times 100\\ &= \left[ {\dfrac{{23326}}{{8115}} - 1} \right] \times 100\\ &= 187\;\% \end{align*} {/eq}


Learn more about this topic:

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Exponential Growth: Definition & Examples

from High School Algebra I: Help and Review

Chapter 6 / Lesson 10
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