2. Find the differential equation of all straight lines at 2- unit distance from the origin.

5. When interest is compounded, the interest earned is added to the principal amount so that it may also earn interest. For a 1-year period, the principal amount Q is given by n i Q = (₁ + ²+ )" n Q (0) where i is the annual interest rate (given as a decimal) and n is the number of times during the year that the interest is compounded. Modeling with a Differential Equation tights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). sed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. To lure depositors, banks offer to compound interest at different intervals: semi- annually, quarterly, or daily. A certain bank advertises that it compounds interest con- tinuously. If $100 is deposited initially, formulate a mathematical…

5. A population of butterflies is released into a den and is growing according to the logistic equation. Suppose that the carrying capacity is 800 butterflies with a relative growth rate of k = 0.2 per month. Write the differential equation describing the logistic population model for this problem.