Chapter 13 – 3 Differential Equations; Growth and Decay Example 1. $1,000 is deposited into an interest bearing account. Find the amount in the account after t years if the rate of change of the amount in the account with respect to time is 8% times the amount in the account. Exponential Growth Law If and then Example 2. Find the amount A in an account after t years if Example 3. The marginal price dp/dx at x units of demand per week is proportional to the price p. If there is no weekly demand at a price of $100 per unit and a weekly demand of 5 units at a price of $77.88 per unit, find the price-demand equation. What price corresponds to a demand of 10 units per week? per unit Example 4. A company is trying to expose a new product to as many people as possible through television advertising. Suppose that the rate of exposure to new people is proportional to the number of potential viewers who have not yet seen the television advertisement. Also, suppose that after 10 days, 40% of the potential viewers have seen the ad. A) Find the function N(t) that gives the number of potential viewers that will have seen the advertisement after t days. Let M represent the number of potential viewers.
Chapter 13 – 3 Differential Equations; Growth and Decay Example 1. $1,000 is deposited into an interest bearing account. Find the amount in the account after t years if the rate of change of the amount in the account with respect to time is 8% times the amount in the account. Exponential Growth Law If and then Example 2. Find the amount A in an account after t years if Example 3. The marginal price dp/dx at x units of demand per week is proportional to the price p. If there is no weekly demand at a price of $100 per unit and a weekly demand of 5 units at a price of $77.88 per unit, find the price-demand equation. What price corresponds to a demand of 10 units per week? per unit Example 4. A company is trying to expose a new product to as many people as possible through television advertising. Suppose that the rate of exposure to new people is proportional to the number of potential viewers who have not yet seen the television advertisement. Also, suppose that after 10 days, 40% of the potential viewers have seen the ad. A) Find the function N(t) that gives the number of potential viewers that will have seen the advertisement after t days. Let M represent the number of potential viewers.