Final answer:
To write an equation for the function that gives the card value based on the number of transactions, use the equation: Card value = m*Number of transactions + b. 'm' represents the rate of increase in card value per transaction, and 'b' represents the starting value of the card.
Step-by-step explanation:
To write an equation for the function that gives the card value based on the number of transactions, we need to identify the relationship between the two variables. It is mentioned that Mike offers a frequent-buyers card, so the more transactions a customer makes, the higher the value of the card. This suggests a linear relationship between the number of transactions and the card value.
Let's assume that the card value increases by a fixed amount each time a transaction occurs. We can represent this with the equation:
Card value = m*Number of transactions + b
where 'm' represents the rate of increase in card value per transaction, and 'b' represents the starting value of the card.
For example, if the rate of increase is $5 per transaction and the starting value is $10, the equation would be:
Card value = 5*Number of transactions + 10