When $1000 is invested at r% interest (compounded continuously) for 10 years, the balance is f (r) dollars, where f is the function shown in Fig. 3.

(a) What will the balance be at 7% interest?

(b) For what interest rate will the balance be $3000?

(c) If the interest rate is 9%, what is the growth rate of the balance with respect to a unit increase in interest?

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4000 3000 2000 Y 1000 y = f(r) y = f'(r) 1 Figure 3 Effect of interest rate on balance. 3 5 7 9 11 13 r