Bank account C starts with 10 and doubles each week. Bank account D starts with 1,000 and grows by $500 each week. When will account C contain more money than account D? Explain your reasoning.

by the 11 week account C would have more money than account D

Step-by-step explanation:

account c would have more money because account c is doubling from the previous amount whereas acount d is just adding 500 to the previoous amount.

VIUSAL REPRENSATION-

Account C- 10$ (1 week) 20$ (2nd week) 40$(3 week) 80$(4 week) 160$(5 week)320$(6 week) 640$(7 week) 1280$(8 week) 2560$( 9 week) 5120$(10 week) 10240$( 11 week)

Account D- 1000$(1 week) 1500$(2 week) 2000$(3 week) 2500$(4 week) 3000$(5 week) 3500$(6 week) 4000$(7week) 4500$(8 week) 5000$(9 week) 6000$(10 week) 6500$(11 week)

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}

lol

step-by-step explanation: