Translate the English statement into a differential equation. Be sure to specify what your variables are.
Tamara spends $40 per week.
There are a couple of ways to do this problem. The two variables involved are money M and time t. We know that Tamara's money is decreasing at a rate of $40 dollars per week. If we let t be measured in weeks we get the differential equation
Alternatively, we could calculate that Tamara spends 40 × 52 = 2080 dollars per year, let t be measured in years, and write
In either case, we need the negative sign because Tamara's money is decreasing, meaning the rate of change of her money with respect to time is negative.