Question

(Score for Question 1: of 5 points)

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1. Susie has a cupcake shop, which opened in 2015. The amount of money her shop earns is represented by
g(x) = 12√x+1 where x is the number of years since 2015. How many years after 2015 will the shop need
to be open in order for her to earn $36?
Please show all work in writing and solving the equation.

Answer 1

x = 26 years

Explanation:

For my class the problem was a little different. It was: g(x) =
`12\sqrt[3]{x+1}`.

Susie has a cupcake shop, which opened in 2015. The amount of money her shop earns is represented by g(x) =
`12\sqrt[3]{x+1}` where x is the number of years since 2015. How many years after 2015 will the shop need to be open in order for her to earn $36?

You replace g(x) with the amount of money.

36 =
`12\sqrt[3]{x+1}`

You have to isolate the cube root. Divide both sides by 12.

`(36)/(12)` =
`\frac{12\sqrt[3]{x+1}}{12}`

So you're left with:

3 =
`\sqrt[3]{x+1}`

Now you need to get rid of the cube.

3³ = (
`\sqrt[3]{x+1}`)³

3³ is the same as 3 * 3 *3 = 27

27 = x + 1

Subtract 1 from both sides.

27 - 1 = x +1 - 1

x = 26 years

Answer 2

Susie has a cupcake shop, which opened in 2015. The amount of money her shop earns is represented by

g(x) = 12√x+1 where x is the number of years since 2015. How many years after 2015 will the shop need

to be open in order for her to earn $36?

Please show all work in writing and solving the equation.

We want to find the number of years after 2015 (let's call it "y") that Susie's cupcake shop needs to be open to earn $36. To do that, we need to solve the equation:

g(x) = 12√x+1 = 36

First, we'll simplify the right side of the equation:

12√x + 1 = 36

Next, we'll subtract 1 from both sides:

12√x = 35

Now, we'll divide both sides by 12:

√x = 35/12

Next, we'll square both sides:

x = (35/12)^2

Finally, we'll calculate the value of x:

x = (35/12)^2 = (35/12)*(35/12) = 35^2 / 12^2 = 1225 / 144 = 25/3

So, the shop needs to be open for 25/3 years after 2015 in order to earn $36. To convert this answer to a whole number of years, we can round up to 9 years.

Therefore, the shop needs to be open for 9 years after 2015 in order to earn $36