Between 2005 and 2010 the average rate of inflation was about 3.3 percent per year if a cart of groceries cost 150 dollars in 2005 what did it cost in 2010

The products did cost $173.9 in 2010

Step-by-step explanation:

Exponential function

Two variables y and x are related as an exponential function if they comply:

where C is the initial value of F, r is the ratio, and k is a proportional constant.

The situation described in the question is modeled as

Where F is the final value of the cart of groceries in 2010, C = $150 is its value in 2005, r is the yearly rate of increase. n is the number of years

. So

If we set n=5 (from 2005 to 2010):

The products did cost $173.9 in 2010

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}

equal to

step-by-step explanation: