17. You invest $4000 in an account to save for college.
a. Option 1 pays 5% annual interest compounded semi-annually. What would
be the balance in the account after 2 years?
b. Option 2 pays 4.5% annual interest compounded continuously. What would
be the balance in the account after 2 years?
c. At what time t (in years) would Option 1 give you $100 more than Option 2?

a. $4,415.25

b. $4,376.70

c. 2.27986 years

Step-by-step explanation:

a.

A = 4,000 (1 + 0.05/2)^(2 x 2)

   = $4,415.25

b.

A = 4,000 x e^(0.045 x 2)

   = $4,376.70

c. $100 more than option 2 = 4,376.70 + 100

                                              = $4,476.70

t (in years) = ln(4,476.70/4,000) /  ln(1 + 0.05/2)

                 = 2.27986 years

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8

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.