Michael has a bank account that he is using to save money to buy a new bike. He hopes to save more and more money each week. The equation that models the situation is y=50(1.5)^x where x is the number of weeks and y is the total amount of money he has saved. What do the 50 and 1.5 mean in the context of the situation? (Hint: One of the numbers involves a percent!)

50 is the initial bank account balance of $50

1.5 represents that his balance grows by 50% (1.5x) each month, or in other words that he deposits 50% of his previous month's balance into his account each month.

i'm going to search it

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}