American University Linear Relationship in Mathematical Problems Questions

EXAM 1
REVIEW
𝑥
𝑦
1
5
3 5 6 7
11 17 20 23
Could the above data be linear? If so,
what’s the slope? If not, explain why.
𝑥
𝑦
1
5
3 5 6 7 20
11 17 20 23 ?
If the above relationship is linear, what
should correspond to 𝑥 = 20?
𝑥
𝑦
1
6
2 3 4
5
16 36 66 106
Could the above data be exponential? If
so, what’s the growth factor? If not,
explain why.
𝑥
𝑦
1 2 3 4 5
81 54 36 24 16
Could the above data be exponential? If
so, what’s the growth factor? If not,
explain why.
𝑥
𝑦
1 2 3 4 5 10
81 54 36 24 16 ?
If the above relationship is exponential,
what should correspond to 𝑥 = 10?
You’re buying a car. The dealer offers
you either 10% off the price of your car,
or $2,500 cash back. For what price of
car is the cash back a better deal?
You go out to dinner with some friends
and the bill after 11% tax is exactly
$100. Was your dinner before tax higher
than, lower than, or exactly $89?
You’re buying a shirt that has been
discounted 30%. You have a coupon
that gets you 20% off the discounted
price. Will the total discount you
receive for the shirt be more than, less
than, or exactly 50% of the original
price?
At a farmer’s market, Daisy sells 3
peaches for $5. Mario sells 5 peaches for
$8. Which vendor charges less per
peach?
At a farmer’s market, Daisy sells 3
peaches for $5. Mario sells 5 peaches for
$8. Is there a reason you would buy
from Daisy?
Olive sells 10 bunches of spinach from 7
to 8 AM. Each successive hour, she sells
5 more than she did the previous hour.
How many total bunches of spinach has
she sold by 12 PM?
Vendors Isaac and Steve work together.
Isaac has 75 apples at his stand and
Steve has 57. How many apples does
Isaac have to give to Steve so that they
both have the same number of apples?
Vendor Dre’s expenses for attending this
week’s Farmer’s Market are $250. If he
sells beets for $3 each, how many must
he sell to recoup his expenses?
A company’s starting salary in 2015
was $50,000. Each year, they raise the
starting salary by 3% to keep up with
inflation. What was the starting salary
in 2017?
A company’s starting salary in 2015
was $50,000. Each year, they raise the
starting salary by 3% to keep up with
inflation. Give a simple estimate for the
starting salary in 2020.
A company’s starting salary in 2015
was $50,000. Each year, they raise the
starting salary by 3% to keep up with
inflation. Find the starting salary in
2020.
A particular species of bamboo grows
linearly and rapidly. At 7 AM, the stalk
is 8 inches tall. Two hours later, it is 11
inches tall. How tall is the bamboo stalk
at 12 PM?
A particular species of bamboo grows
linearly and rapidly. At 7 AM, the stalk
is 8 inches tall. Two hours later, it is 11
inches tall. Come up with an equation
that can tell you the bamboo’s height 𝐻
in inches 𝑡 hours after 7 AM.
A particular species of bamboo grows
linearly and rapidly. At 7 AM, the stalk
is 8 inches tall. Two hours later, it is 11
inches tall. At what time of day will the
bamboo reach 2 feet tall?
A particular species of bamboo grows
linearly and rapidly. At 7 AM, the stalk
is 8 inches tall. Two hours later, it is 11
inches tall. Will this equation be able to
predict the bamboo’s height in a year?
A population of 𝑃 bacteria is put in a
petri dish and doubles every 3 hours.
How long will it take for the population
to be 16 times its starting size?
A population of 𝑃 bacteria is put in a
petri dish and doubles every 3 hours. It
takes 60 hours to fill up half of the petri
dish. How much longer will it take until
the petri dish is entirely full?
A population of 𝑃 bacteria is put in a
petri dish and doubles every 3 hours. A
scientist expects the population to stop
growing exponentially after a while.
Does this seem reasonable? If not,
explain what’s wrong.
In a class of 30 students, 18 are from the
East Coast, and 8 are in SIS. How many
students in the class are not from the
East Coast?
In a class of 30 students, 18 are from
the East Coast, and 8 are in SIS. Give
two possible answers to the number of
students in the class that are not from
the East Coast and also not in SIS?
In a class of 30 students, 18 are from
the East Coast, and 8 are in SIS. If we
know that 7 students are not from the
East Coast and also are not in SIS, how
many students are from the East Coast
and also in SIS?
A company that makes t-shirts models
the cost 𝐶, measured in thousands of
dollars, to produce 𝑡 thousand shirts as
𝐶 = 5𝑡 + 25.
What is the slope of the line? Interpret
this slope in terms of the units of the
problem.
A company that makes t-shirts models
the cost 𝐶, measured in thousands of
dollars, to produce 𝑡 thousand shirts as
𝐶 = 5𝑡 + 25.
How much money will it cost to
produce 1000 t-shirts?
A company that makes t-shirts models
the cost 𝐶, measured in thousands of
dollars, to produce 𝑡 thousand shirts as
𝐶 = 5𝑡 + 25.
If you have a budget of $70,000, how
many t-shirts are you able to produce?
SLOW
QUESTIONS
You’re buying $100 worth of stuff from
Bed, Bath, and Beyond. You have two
coupons: one for 20% off, one for 25%
off. The coupons can be combined.
How much will your final bill be? Does
the order of the coupons matter?
You have a 3-liter and a 5-liter water
container; each container has no
markings except for that which gives
you its total volume. You also have a
running tap. You must use the
containers and the tap in such a way as
to measure out exactly 4 liters of water.
How do you do it?
END OF
EPISODE