Question

Choose all of the statements that correctly compare the two functions shown.

Alec's rate of savings is greater than Beth's.

entific

Alec and Beth are saving at the same rate.

Alec started with more money than Beth

mulas

Time

maining

:19:23

Beth started with more money than Alec,

de les

At 10 days, Alec will have $1 more than Beth in savings,

Answer 1

its bc and e or Alec and Beth are saving at the same rate. Alec started with more money than Beth. and At 10 days, Alec will have $1 more than Beth in savings.

Explanation:

Answer 2

b, c and e

Explanation:

Given

See attachment for functions

Required

Select all statements that contain both functions

First, calculate the rate (slope) of both functions.

This is calculated as:

`m = (y_2 - y_1)/(x_2 - x_1)`

For Alec's

`(x_1,y_1) = (0,3)`

`(x_2,y_2) = (2,9)`

So, the slope is:

`m = (9 - 3)/(2 - 0)`

`m = (6)/(2)`

`m =3`

For Beth's

`(x_1,y_1) = (5,17)`

`(x_2,y_2) = (12,38)`

So, the slope is:

`m = (38 - 17)/(12 - 5)`

`m = (21)/(7)`

`m =3`

Beth and Rec have the same slope. Hence, they save at the same rate.

Next, determine the amount they started with.

This implies that we calculate y when x = 0

From Alec's graph.

`(x,y) = (0,3)`

Alec's initial savings is 3

For Beth's savings, we make use of slope formula.

`m = (y_2 - y_1)/(x_2 - x_1)`

`(x_1,y_1) = (5,17)`

`(x_2,y_2) = (0,y)`

So, we have:

`3 =(y - 17)/(0 - 5)`

`3 =(y - 17)/( - 5)`

`y - 17 = -15`

`y = 17 -15`

`y = 2`

Beth's initial savings is 2

Hence, Alec started with more money

Next, is to determine who has more money after 10 days.

Since they save at the same rate, the difference in their savings after any number of days will be the difference in their initial savings.

The difference (d) is calculated as:

`d = 3 - 2`

`d = 1`

Hence, Alec will have $1 more than Beth after 10 days