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

Let's analyze the function \( f(t) = 1.90 + 1.40t \) step by step.

a. Y-Intercept

The y-intercept of a function is the value of the function when the input (in this case, the number of toppings \( t \)) is zero.

For \( f(t) = 1.90 + 1.40t \):

• When \( t = 0 \): \[ f(0) = 1.90 + 1.40(0) = 1.90 \]

Interpretation of the y-intercept: The y-intercept \( 1.90 \) represents the cost of a hamburger with no toppings. So, the base price of the hamburger itself is $1.90.

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b. Slope

The slope of the function indicates how much the function value (cost of the hamburger) increases for each additional topping.

In the function \( f(t) = 1.90 + 1.40t \), the slope is \( 1.40 \).

Interpretation of the slope: The slope \( 1.40 \) means that for each additional topping added to the hamburger, the cost increases by $1.40.

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c. Finding the Number of Toppings

To find the number of toppings \( t \) on Jodi's hamburger when she paid $3.30, we can set the function equal to 3.30 and solve for \( t \):

\[ f(t) = 3.30 \]

Substituting the function into the equation gives:

\[ 1.90 + 1.40t = 3.30 \]

Now, we can solve for \( t \):

1. Subtract \( 1.90 \) from both sides: \[ 1.40t = 3.30 - 1.90 \] \[ 1.40t = 1.40 \]

2. Divide both sides by \( 1.40 \): \[ t = \frac{1.40}{1.40} = 1 \]

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