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Lisa specializes in baking lemon cupcakes. She bakes 3 dozen cupcakes every hour. The cost (in dollars) of making \(n\) cupcakes is given by the function \(C(n)=60+0.45n\).

The function that models the number of cupcakes Lisa makes in \(h\) hours is \(n(h)= \square \).

The cost function in terms of hours, \(h\), is given by \( \square \).

Lisa's cost for making cupcakes for 2 hours is [tex]\( \square \)[/tex].

Sagot :

GinnyAnswer
To solve each part of the problem, let's break it down step-by-step.

1. Modeling the Number of Cupcakes Lisa Makes in \( h \) Hours:
- Lisa bakes 3 dozen cupcakes every hour.
- Since 1 dozen equals 12 cupcakes, Lisa makes \( 3 \times 12 = 36 \) cupcakes each hour.
- Therefore, the number of cupcakes \( n \) that Lisa makes in \( h \) hours is \( 36h \).

So, \( n(h) = 36h \).

2. Cost Function in Terms of Hours, \( h \):
- The cost function of making \( n \) cupcakes is given by \( C(n) = 60 + 0.45n \).
- We want the cost function in terms of hours \( h \).
- We already have \( n(h) = 36h \).
- Substituting \( n = 36h \) into the cost function gives:
[tex]\[ C(n) = 60 + 0.45 \times 36h \][/tex]
Simplifying:
[tex]\[ C(h) = 60 + 16.2h \][/tex]

So, the cost function in terms of hours is \( C(h) = 60 + 16.2h \).

3. Cost for Making Cupcakes for 2 Hours:
- We use the cost function \( C(h) = 60 + 16.2h \) to find the cost for 2 hours.
- Substitute \( h = 2 \) into the cost function:
[tex]\[ C(2) = 60 + 16.2 \times 2 \][/tex]
[tex]\[ C(2) = 60 + 32.4 \][/tex]
[tex]\[ C(2) = 92.4 \][/tex]

So, Lisa's cost for making cupcakes for 2 hours is \( \$92.40 \).

Therefore, the correct answers are:
- The function that models the number of cupcakes Lisa makes in \( h \) hours is: \( n(h) = 36h \).
- The cost function in terms of hours, \( h \), is: \( C(h) = 60 + 16.2h \).
- Lisa's cost for making cupcakes for 2 hours is: [tex]\( \$92.40 \)[/tex].
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