The function below shows the cost of a hamburger with different numbers of toppings (t).

Question

f(t) = 1.90 + 1.40t

a. What is the y-intercept, and what does it mean?

b. What is the slope, and what does it mean?

c. If Jodi paid $3.30 for a hamburger, how many toppings were on Jodi’s hamburger?

Answer 1

To analyze the function \( f(t) = 1.90 + 1.40t \), we need to look at its components:

a. Y-intercept

The y-intercept is the value of the function when \( t = 0 \).

\[ f(0) = 1.90 + 1.40(0) = 1.90 \]

Meaning: The y-intercept, \( 1.90 \), represents the base cost of a hamburger with no toppings. This is the price you pay for just the hamburger itself.

b. Slope

The slope of the function is the coefficient of \( t \), which is \( 1.40 \).

Meaning: The slope indicates the additional cost added for each topping on the hamburger. In this case, each topping costs an additional \( 1.40 \).

c. Finding the number of toppings from the cost

If Jodi paid \( 3.30 \) for a hamburger, we can set up the equation from the function:

\[ f(t) = 3.30 \] \[ 1.90 + 1.40t = 3.30 \]

To find \( t \), we first subtract \( 1.90 \) from both sides:

\[ 1.40t = 3.30 - 1.90 \] \[ 1.40t = 1.40 \]

Now, divide both sides by \( 1.40 \):

\[ t = \frac{1.40}{1.40} = 1 \]

Conclusion: Jodi had \( 1 \) topping on her hamburger.