Question

Kayla runs a lemonade stand at the state fair. She sold 43 cups of lemonade during the first week. If her business grows 3.5% each week, how many cups of lemonade can she expect to sell 4 weeks later?

Which exponential function rule represents Kayla's business?

Answer 1

4(43)^3.5 Set up an exponential equation

Answer 2

`f(x)=43(1.035)^x`

Explanation:

Given,

The number of cups she sold in first week = 43,

Also, her business grows 3.5% each week,

So, the number of cups she sold in second week = (100+3.5)% of 43

= 103.5% of 43

= 1.035(43),

In third week = 103.5% of 1.035(43) = 1.035²(43),

In fourth week = 103.5% of 1.035²(43) = 1.035³ (43),

.........., so on,

Thus, the number of cups she will sold after x + 1 weeks or x weeks later from the first week =
`1.035^x (43)`

If f(x) represents the number of cups x weeks later,

`\implies f(x)=43(1.035)^x`

Which is the required function rule that represents her business.

Also, if x = 4,

The number of cups she will sell 4 weeks later,

`f(4)=43(1.035)^4=49.3434890269\approx 49`