Let's break down the problem step by step.

The cost function for the cab ride is given by the equation:

$C(t) = 1.45t + 3.25$

Where:

• $t$ is the number of minutes of the cab ride.
• $C(t)$ is the total cost in dollars.

Question 1: Cost of a 37-minute ride

You are asked to find the cost of a 37-minute ride.

Substitute $t = 37$ into the formula:

$C(37) = 1.45(37) + 3.25$

I'll calculate that for you.

Question 2: Base cost (even without any ride)

The base cost is the constant term in the equation, which is the amount you must pay just to get into the cab. The constant here is $3.25$, so the base cost is $3.25.

Question 3: Which part of the formula tells you the base cost?

The base cost is represented by the constant 3.25, which is the fixed amount added to the total cost regardless of the number of minutes.

Question 4: How much does each additional minute add?

The cost per additional minute is represented by the coefficient of $t$ in the equation, which is 1.45. This means every additional minute adds $1.45 to the total cost.

Question 5: Which part of the formula tells you this information?

The part of the formula that tells you the cost per additional minute is the coefficient 1.45, which is multiplied by the number of minutes $t$.

Let me now calculate the cost for 37 minutes.The cost for a 37-minute cab ride would be $56.90.

Would you like more details or have any questions about this problem?

Here are some related questions:

1. What would the cost be for a 50-minute ride using the same formula?
2. If the base cost increased to $4.00, how would that change the total cost for a 37-minute ride?
3. How would the total cost change if the cost per minute was reduced to $1.30?
4. How many minutes would a ride take if the total cost was $70.00?
5. If a person only had $30, how many minutes could they afford?

Tip: In linear functions, the coefficient of the variable represents the rate of change per unit, while the constant represents the initial or fixed value.