Level curves of a savings account Suppose you make a one-time deposit of P dollars into a savings account that earns interest at an annual rate of p% compounded continuously. The balance in the account after t years is B(P, r, t) = Pert, where r = p/100 (for example, if the annual interest rate is 4%, then r = 0.04). Let the interest rate be fixed at r = 0.04.a. With a target balance of $2000, find the set of all points (P, t) that satisfy B = 2000. This curve gives all deposits P and times t that result in a balance of $2000.b. Repeat part (a) with B = $500, $1000, $1500, and $2500, and draw the resulting level curves of the balance function.c. In general, on one level curve, if t increases, does P increase or decrease?
Level curves of a savings account Suppose you make a one-time deposit of P dollars into a savings account that earns interest at an annual rate of p% compounded continuously. The balance in the account after t years is B(P, r, t) = Pert, where r = p/100 (for example, if the annual interest rate is 4%, then r = 0.04). Let the interest rate be fixed at r = 0.04.
a. With a target balance of $2000, find the set of all points (P, t) that satisfy B = 2000. This curve gives all deposits P and times t that result in a balance of $2000.
b. Repeat part (a) with B = $500, $1000, $1500, and $2500, and draw the resulting level curves of the balance function.
c. In general, on one level curve, if t increases, does P increase or decrease?
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