Andrew deposited $500 in a savings account that offers an interest rate of 6.5%, compounded continuously.
andrew's initial deposit will grow to $543 in
months.

Time in months ≈ 16 months

Step-by-step explanation:

Principal Amount = $500

Interest Rate = 6.5%

Amount = $543

n = Number of times the interest is compounded

⇒ n = 12 ( because given that the interest is compounded continuously)

We need to calculate Time in months :

So, Time in months = 1.28 × 12

                                  ≈ 16 months

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.