The function c(t)=c0(1+r)ᵗ models the rise in the cost of a product that has a cost of c0 today, subject to an average yearly inflation rate of r for t years. If the average annual rate of inflation over the next 8 years is assumed to be 1.5%, what will the inflation-adjusted cost of a $383 bicycle be in 8 years? Round to two decimal places.

Question

The function c(t)=c0​(1+r)ᵗ models the rise in the cost of a product that has a cost of c0​ today, subject to an average yearly inflation rate of r for t years. If the average annual rate of inflation over the next 8 years is assumed to be 1.5%, what will the inflation-adjusted cost of a $383 bicycle be in 8 years? Round to two decimal places.

Bot GPT 3.5 · Answer

The inflation-adjusted cost of a product can be calculated using the formula c(t) = c0 * (1 + r)^t, where c0 is the current cost, r is the average yearly inflation rate, and t is the number of years. In this case, c0 = $383, r = 1.5% = 0.015, and t = 8 years. Using the formula, we have: c(t) = 383 * (1 + 0.015)^8 c(t) = 383 * (1.015)^8 c(t) = 383 * 1.127659574468085 c(t) ≈ 431.92 Therefore, the inflation-adjusted cost of the $383 bicycle in 8 years will be approximately $431.92.