Section 4.8: Function Applications
Functions are used to model real-life situations, such as calculating costs, distances, populations, or temperatures. Understanding how to interpret and apply function rules is essential.
Example 1
A taxi charges a base fee of $3 plus $2 per mile. Write a function for the total cost \( C(x) \) and find the cost for a 5-mile ride.
Function: \( C(x) = 2x + 3 \)
Cost for 5 miles: \( C(5) = 2(5) + 3 = 13 \) dollars
Example 2
The temperature in °F is given by \( F(t) = 1.8t + 32 \) where \( t \) is in °C. Find \( F(25) \).
\( F(25) = 1.8(25) + 32 = 77 \) °F
Practice Problems
- A phone plan charges $10 plus $0.05 per text. Write the function and find the cost for 100 texts.
- A car rental costs $40 per day plus $0.20 per mile. Find the total cost for 3 days and 150 miles.
- The value of a computer decreases by $200 each year. Write a function for its value and find it after 4 years.
- The population of a town grows by 5% each year. Write a function for the population and find it after 3 years given 1,000 people initially.
- A factory produces \( P(x) = 50x + 200 \) units per day. Find the production after 8 days.