Match each polynomial function with one of its factors. f(x) = x3 − 3x2 − 13x + 15 f(x) = x4 + 3x3 − 8x2 + 5x − 25 f(x) = x3 − 2x2 − x + 2 f(x) = -x3 + 13x − 12 x − 2 --> x + 3 --> x + 4 --> x + 5 -->

Step-by-step explanation:

The value of a function will be zero if the factor is put in it. In order to check whether a factor is of a function or not we will put the value of x from that factor in the function:

So

x-2 = 0 => x=2

Putting in first function

So x-2 is not a factor of first function.

Putting in second function

So x-2 is also not a factor of second function.

Putting in third function:

So x-2 is factor of third function.

...........................

For x+3

x+3=0

x=-3

First function:

So x+3 is a factor of first function.

.............................

For x+4

x+4=0

x=-4

As we have already found the factors of first and third function, we will now only check second and fourth function.

So x+4 is not a factor of second function.

Putting in fourth function:

So x+4 is a factor of fourth function

..........................

For x+5=0

x=-5

Since only one function is remaining we'll only check for that.

the correct answer is you spend $55.78 more in a brand store that buy ing in a normal store.

step-by-step explanation:

brand = spend   $ 135.85 total

store = spend $80.07 total

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

=====================================

part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

=====================================

part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).