Identify Initial Values & Calculate Rates of Change in Real Scenarios

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. What is the initial value, and what is the rate of change per mile?

• Initial value: $70, Rate of change per mile: $0.20

• Initial value: $30, Rate of change per mile: $0.10

• Initial value: $50, Rate of change per mile: $0.20

• Initial value: $50, Rate of change per mile: $0.50

A phone plan costs $30 per month plus $0.10 for each text message sent. Identify the initial value and calculate the rate of change for each text message.

• Initial value: $30, Rate of change: $0.10 per text message

• Initial value: $30, Rate of change: $0.20 per text message

• Initial value: $40, Rate of change: $0.10 per text message

• Initial value: $20, Rate of change: $0.05 per text message

A bakery sells cupcakes for $3 each and has a starting cost of $15 for ingredients. What is the initial value, and how much does the cost increase per cupcake sold?

• Initial value: $15, Cost increase per cupcake sold: $0

• Initial value: $20, Cost increase per cupcake sold: $3

• Initial value: $10, Cost increase per cupcake sold: $1

• Initial value: $15, Cost increase per cupcake sold: $2

A gym membership has an initial fee of $25 and a monthly fee of $15. What is the initial value, and how does the total cost change each month?

• Initial value: $15; Monthly change: $25

• Initial value: $25; Monthly change: $15

• Initial value: $25; Monthly change: $10

• Initial value: $30; Monthly change: $15

A water tank starts with 500 liters and drains at a rate of 5 liters per hour. What is the initial value of the water in the tank, and how does the volume change over time?

• The initial value is 600 liters; the volume changes as 600 - 5*t liters over time.

• The initial value is 500 liters; the volume changes as 500 + 5*t liters over time.

• The initial value is 500 liters; the volume changes as 500 - 5*t liters over time.

• The initial value is 500 liters; the volume increases by 5 liters per hour.

A subscription service charges $10 for the first month and $5 for each additional month. Identify the initial value and calculate the rate of change for each additional month.

• Initial value: $10, Rate of change: $5 per month

• Initial value: $15, Rate of change: $5 per month

• Initial value: $5, Rate of change: $10 per month

• Initial value: $10, Rate of change: $2 per month

A school sells tickets for a play at $8 each, with an initial cost of $50 for the venue. What is the initial value, and how does the total cost change with each ticket sold?

• Initial value is $50; total cost remains $50, total revenue increases by $8 per ticket.

• Initial value is $0; total cost increases by $8 per ticket.

• Initial value is $50; total revenue decreases by $8 per ticket.

• Initial value is $50; total cost increases by $50 per ticket sold.

A bike rental shop charges $15 for the first hour and $5 for each additional hour. What is the initial value, and how does the cost change with each additional hour?

• Initial value is $15; cost decreases by $5 for each additional hour.

• Initial value is $15; cost increases by $5 for each additional hour.

• Initial value is $20; cost increases by $7 for each additional hour.

• Initial value is $10; cost increases by $3 for each additional hour.

A concert ticket costs $50, and there is a service fee of $10. What is the initial value, and what is the rate of change if you buy more tickets?

• Initial value: $60, Rate of change: $10 per ticket

• Initial value: $60, Rate of change: $50 per ticket

• Initial value: $70, Rate of change: $60 per ticket

• Initial value: $50, Rate of change: $10 per ticket

A delivery service charges a base fee of $20 plus $2 per mile. Identify the initial value and calculate the rate of change per mile driven.

• Initial value: $20, Rate of change: $5 per mile

• Initial value: $20, Rate of change: $2 per mile

• Initial value: $25, Rate of change: $1 per mile

• Initial value: $15, Rate of change: $3 per mile