Question

The functions below show the amount of money Bella and Sweet T had saved after earning money for doing chores. Which description best compares the two functions?

Answer 1

Answer:

Bella saves more per chore than Sweet T.

Answer 2

Answer:

Bella saves more per chore than Sweet T

Step-by-step explanation:

Amount of money Bella saved : $d=3.5c+11$

where d represents savings

c represents number of chores

11 represents initial value

Sweet T saved :

Number of chores (c)      Savings (d)

         1                                  12

         2                                 14

         3                                 16

         4                                 18

         5                                 20

So, equation of amount saved by sweet T can be formed using two point slope form :

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$(x_1,y_1)=(1,12)$

$(x_2,y_2)=(2,14)$

Substituting the values in equation :

$y-12=\frac{14-12}{2-1}(x-1)$

$y-12=2x-2$

$y=2x+10$

y represents the amount she saved

x represents the number of chores .

So, equation of amount saved by sweet T : $d=2c+10$

option 1:The initial value of Bella is less than initial value of Sweet T

11 is not less than 10

Hence Option 1 is wrong.

Option 2: After both have done 5 chores Sweet T has saved more

Bella's equation : $d=3.5c+11$

At c = 5 , $d=3.5\times 5+11 =28.5$

Sweet T 's equation :$d=2c+10$

At c = 5 , $d=2\times 5+10 =20$

Bella saved more .

Hence Option 2 is wrong.

Option 3: Bella saves more per chore than Sweet T

Bella's equation : $d=3.5c+11$

At c = 1 , $d=3.5\times 1+11 =14.5$

Sweet T 's equation :$d=2c+10$

At c =1 , $d=2\times1+10 =12$

Bella save more per chore

Hence Option 3 is right

Option 4: Sweet T's saving increase at faster rate than Bella's

Equation of line : y=mx+c

where m is the slope which tells us about the rate .

Bella's equation : $d=3.5c+11$

Sweet T 's equation :$d=2c+10$

At c =1 , $d=2\times1+10 =12$

Bella save more per chore

Comparing both equations with equation of line

Bella's m = 3.5

Sweet T's m = 2

Thus Bella's saving increase at faster rate than Sweet T's.

Hence Option 4 is wrong.