The amount of fertilizer in a landscaping company's warehouse decreases at a rate of 2% per week. The amount of fertilizer in the warehouse was originally, `64,000` cubic yards. Which function models the amount of fertilizer in cubic yards left after `w` weeks?
The amount of fertilizer in the warehouse decreases at a rate of 2% per week. This means that after each week, the amount of fertilizer left in the warehouse is only 98% of what it was the previous week.
Let's start with the original amount of fertilizer in the warehouse, which is 64,000 cubic yards. After 1 week, the amount of fertilizer left in the warehouse is 98% of 64,000, or 0.98 * 64,000. After 2 weeks, the amount left is 98% of that amount, or 0.98 * 0.98 * 64,000.
In general, after `w` weeks, the amount of fertilizer left can be expressed as `64000 * 0.98^w`.
Therefore, the function that models the amount of fertilizer in cubic yards left after `w` weeks is:
F(w) = 64000 * 0.98^w