Question

Tony is spending money at a constant rate.

Suppose he initially has $1000, and after 4 months, he has $760.
a) Interpret the rate at which Tony's amount of money is changing?
b) Express the amount of money he has, A(m), as a linear function of the number of months, in
c) How long will it take Tony to have no money?

Answer 1

Tony is spending money at a rate of $60 per month, as determined from his initial $1000 to $760 after 4 months. His amount of money as a function of time, A(m), is A(m) = 1000 - 60m. It will take Tony approximately 16.67 months to have no money left.

Step-by-step explanation:

To determine the rate at which Tony's amount of money is changing, we observe that Tony starts with $1000 and then has $760 after 4 months. This means he has spent $240 over 4 months, so the rate of change is $240/4 months = $60 per month.

To express Tony's amount of money as a linear function of the number of months, A(m), we set up the equation based on the initial value (intercept) and the rate of change (slope). Therefore, A(m) = 1000 - 60m, where m represents the number of months.

Finally, to determine how long it will take for Tony to have no money, we need to find when A(m) equals zero. Solving the equation 0 = 1000 - 60m tells us that m = 1000/60, which simplifies to approximately 16.67 months. So, it will take Tony just under 17 months to spend all his money at the current rate.