You earned $1600 in interest in your savings account over 10 years at a rate of 8%. How much money did you originally deposit into your savings account?

A = p(1+r)^t

1600 = p(1+0.08)¹⁰

P = 1600/2.1589

P= 741.12

741.12 dollar money did you originally deposit into your savings account!

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.