4 − (x + 2) < −3(x + 4)

x<-7

Step-by-step explanation:

4 − (x + 2) < −3(x + 4)

4 − x - 2< −3x - 12

14 < - 2x

x<-7

Answer and Step-by-step explanation:

First, we need to solve both sides of the equation.

Distribute the negative to the x and the 2.

4 - x - 2 < -3(x + 4)

Distribute the -3 to the x and the 4.

4 - x - 2 < -3x - 12

Combine like terms.

2 - x < -3x - 12

Add 12 to both sides of the equation.

12 + 2 - x < -3x - 12 + 12

14 - x < -3x

Add x to both sides of the equation.

14 - x + x < -3x + x

14 < -2x

*Divide both sides of the equation by -2, and flip the sign.

-7 > x

-7 > x is the answer.

*How this works:

When we flip the sign, we really are just saving ourselves an extra step when dividing numbers (that are negative, only works when number is negative).

14 < -2x

If we were to add to x, and subtract 14, it will look like this:

2x < -14

Then when we divide by 2, we get:

x < -7

This is the same result, but it takes an extra step. Use this way if you forget why you need to flip the sign when dividing by a negative number.

#teamtrees #PAW (Plant And Water)

I hope this helps!

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)

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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

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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).

answer: 88

step-by-step explanation: