Joseph joins a gym that charges $79.99 per month plus tax for a premium membership. A tax of 6% is applied to the monthly fee. Joseph is also charged a one-time initiation fee of $95 as soon as he joins. There is no contract so that Joseph can cancel at any time without having to pay a penalty. Which of the following represents Joseph’s total charge, in dollars, if he keeps his membership for t months?

Options

A. `1.06(79.99+95)t`
B. `1.06(79.99t+95)`
C. `(1.06*79.99t)+95`
D. `(79.00+.06t)+95`

Answer

To find Joseph's total charge for keeping his gym membership for \( t \) months, we can break down the costs involved:

1. **Monthly Membership Fee**: The gym charges \( 79.99 \) dollars per month.
2. **Tax on Monthly Fee**: There is a tax of \( 6\% \) applied to the monthly fee. Therefore, the total monthly cost including tax can be calculated as follows:
\[ \text{Total Monthly Cost} = \text{Monthly Fee} + \text{Tax} = 79.99 + 0.06 \times 79.99 \]

3. **Calculating the Tax**:
\[ \text{Tax} = 0.06 \times 79.99 = \frac{6}{100} \times 79.99 = 4.7994 \]
So, the total monthly cost including tax is:
\[ \text{Total Monthly Cost} = 79.99 + 4.7994 = 84.7894 \]

4. **Total Cost for \( t \) Months**: The total cost for \( t \) months is:
\[ \text{Total Cost for } t \text{ months} = 84.7894 \times t \]

5. **One-Time Initiation Fee**: Joseph also has to pay a one-time initiation fee of \( 95 \) dollars when he joins the gym. This fee is not multiplied by \( t \) since it is a one-time payment.

6. **Total Charge**: Thus, the total charge \( C \) for Joseph after \( t \) months will be:
\[ C = (84.7894 \times t) + 95 \]

7. **Simplifying the Expression**: We can factor out the monthly cost:
\[ C = 79.99 \times (1 + 0.06) \times t + 95 = 79.99 \times 1.06 \times t + 95 \]
This simplifies to:
\[ C = 79.99 \times 1.06^t + 95 \]

Thus, the final expression representing Joseph's total charge if he keeps his membership for \( t \) months is:
\[ C = 79.99 \times 1.06 \times t + 95 \]