Question

Meg's family and friends gave her a total of $200 for her birthday. She wants to use the money to buy vintage T-shirts, which cost $16 each. You can use a function to describe the amount of birthday money Meg has left after purchasing x T-shirts. Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)x. h(x)=

Answer 1

To describe the amount of birthday money Meg has left after purchasing \( x \) vintage T-shirts, we will create a linear function.

Meg starts with a total of $200 and spends $16 for each T-shirt she buys. Therefore, the amount of money left after buying \( x \) T-shirts can be expressed as:

\[
h(x) = 200 - 16x
\]

In this function:
- \( h(x) \) represents the amount of money Meg has left after buying \( x \) T-shirts.
- The coefficient \( -16 \) (the slope) indicates how much money is subtracted for each T-shirt purchased.
- The constant \( 200 \) (the y-intercept) is the initial amount of birthday money she has.

Thus, the function is linear, and in the form \( h(x) = mx + b \), it is presented as:

\[
h(x) = -16x + 200
\]

Here, \( m = -16 \) and \( b = 200 \).