If you open a bank account with a $200 starting balance and it earns 2.5% interest, compounded annually, how much interest will you earn in 10 years?

  $56.02

Step-by-step explanation:

The account balance after 10 years is given by the future value formula:

  FV = P(1 +r)^t . . . . . principal P invested at rate r compounded annually for t years

  FV = $200(1 +0.025)^10 ≈ $256.02

The amount in excess of the original investment is the interest earned:

  $256.02 -200.00 = $56.02 . . . . interest earned in 10 years

$256.02

Step-by-step explanation:

Here is the formula: 200(1.025)^10.

The .025 is the percentage of the interest, and the 1 is the money you already have (which is 200). The ^10 is the 10 years.

If you take the (1.025)^10, you'll get an incredibly large number, 1.2800

Take that large number and multiply it by the amount of money you originally have, $200. Then you'll get something like 256.0169... Round to the near hundredth, and you'll have 256.02

b

step-by-step explanation:

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.