If $3,500 is invested at an interest rate of 6.25% per year compounded continuously, find the value of the investment after (a) 3 years, (b) 6 years, and (c) 9 years. (the formula can be found in the lecture notes or the textbook.)

(a) 3 years FV=$4,221.80

(b) 6 years FV=$5,092.46

(c) 9 years FV=$6,142.69

Step-by-step explanation:

The formula for continuously compounded interest is

FV = PV x e^(i x t)

where,

FV=future value of the investment,

PV= present value,

i = stated interest rate,

t = time in years,

e= mathematical constant approximated as 2.7183.

In this case,  

PV=$3,500

i = 6.25%

(a) 3 years

FV = PV x e^(i x t)

FV = $3,500 x e^(6.25%x3)

FV=$4,221.80

(b) 6 years

FV = $3,500 x e^(6.25%x6)

FV=$5,092.46

(c) 9 years

FV = $3,500 x e^(6.25%x9)

FV=$6,142.69

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.