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

Question

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

GPT-4o mini · Answer

Let's analyze the function $ f(t) = 1.90 + 1.40t $ step by step. ### a. Y-Intercept The y-intercept occurs when $ t = 0 $. By substituting $ t = 0 $ into the function: $$ f(0) = 1.90 + 1.40(0) = 1.90 $$ **Interpretation**: The y-intercept of 1.90 means that the cost of a hamburger with no toppings (t = 0) is $1.90. ### b. Slope The slope of the function is the coefficient of $ t $, which is 1.40. **Interpretation**: The slope of 1.40 indicates that for each topping added to the hamburger, the cost increases by $1.40. ### c. Determine the number of toppings for Jodi's hamburger We know that Jodi paid $3.30 for her hamburger. We can set up the equation using the function: $$ f(t) = 3.30 $$ $$ 1.90 + 1.40t = 3.30 $$ Now, we 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's hamburger had **1 topping**.