Question

multiple choice
for exercises 1 - 5, choose the correct letter.

1. jill earns $45 per hour. using $p$ for her pay and $h$ for the number of hours she works, what function rule represents the situation?

a. $h = 45p$ b. $p = 45h$ c. $h=p + 45$ d. $p=h + 45$

1. what is a function rule for the perimeter $p$ of a building with a rectangular base if the width $w$ is two times the length $ell$?

f. $p = 2ell$ g. $p = 2w$ h. $p = 6ell$ j. $p = 6w$

1. a triangle has a base $b$ that is 8 in. longer than twice the height $h$. which function rule can be used to represent the area of the triangle in terms of the height?

a. $a=\frac{1}{2}bh$ b. $a=\frac{1}{2}h(h + 8)$ c. $a=h^{2}+4h$ d. $a=\frac{1}{2}(2h)(h + 8)$

1. which equation represents the sentence “$d$ is 17 less than the quotient of $n$ and 4”?

f. $d=\frac{n}{4}-17$ g. $d=\frac{n}{4}+17$ h. $d = 4n-17$ j. $d-17=\frac{n}{4}$

1. the function rule for the profit a company expects to earn is $p = 1500m+2700$, where $p$ represents profit and $m$ represents the number of months the company has been in business. how much profit should the company earn after 12 months in business?

a. $15,700$ b. $17,700$ c. $18,000$ d. $20,700$
extended response

1. a plane was flying at an altitude of 30,000 feet when it began the descent toward the airport. the plane descends at a rate of 850 feet per minute.

a. what is the function rule that describes this situation?
b. what is the altitude of the plane after it has descended for 8 minutes? show your work.
c. use the function in part (a) to determine how long, to the nearest minute, it takes for the plane to land if it descends at a constant rate.

Explanation:

Step1: Analyze problem 1

Pay $p$ is $45$ times hours $h$, so $p = 45h$. Answer is B.

Step2: Analyze problem 2

If width $w = 2l$, perimeter of rectangle base $P=2(l + w)=2(l + 2l)=6l$. Also $P = 3w$. But if we express in terms of $l$ only among given options, answer is H.

Step3: Analyze problem 3

Base $b=2h + 8$, area of triangle $A=\frac{1}{2}bh=\frac{1}{2}(2h + 8)h=h^{2}+4h$. Answer is C.

Step4: Analyze problem 4

$d$ is 17 less than $\frac{n}{4}$, so $d=\frac{n}{4}-17$. Answer is F.

Step5: Analyze problem 5

Substitute $m = 12$ into $P = 1500m+2700$, $P=1500\times12 + 2700=18000+2700=20700$. Answer is D.

Step6: Analyze problem 6 - a

Initial altitude is 30000, descends at 850 per minute. Function rule is $A(t)=30000 - 850t$ where $A(t)$ is altitude and $t$ is time in minutes.

Step7: Analyze problem 6 - b

Substitute $t = 8$ into $A(t)=30000 - 850t$, $A(8)=30000-850\times8=30000 - 6800=23200$ feet.

Step8: Analyze problem 6 - c

Set $A(t)=0$, $0 = 30000-850t$, $850t=30000$, $t=\frac{30000}{850}\approx35$ minutes.

Answer:

1. B. $p = 45h$
2. H. $P = 6l$
3. C. $A=h^{2}+4h$
4. F. $d=\frac{n}{4}-17$
5. D. $\$20,700$
6. a. $A(t)=30000 - 850t$

b. 23200 feet
c. 35 minutes