Mrs. Williams put $500 into a retirement account that earns 4% interest. How long will it take for there to be $3,500? What is the A value?
What is the B value?
What is the equation and answer?

9514 1404 393

  A = 500

  B = 1.04

  49.6 years

Step-by-step explanation:

We assume your 'A' and 'B' refer to parameters in an exponential formula of the form ...

  y = A·B^x

In this form, A is the initial investment value, $500. B is the growth factor, 1+4% = 1.04, assuming interest is compounded annually. We want to find x such that y=$3500.

  3500 = 500·1.04^x . . . . . fill in known values

  7 = 1.04^x . . . . . . . . . . . . . divide by 500

  log(7) = x·log(1.04) . . . . . . take logarithms

  x = log(7)/log(1.04) ≈ 49.61 . . . . divide by the coefficient of x

It will take about 49.6 years for there to be $3500 in Mrs. Williams's account.

b

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}