Math 1
Unit 5 Review
1.
Name__________________________________
Hypothermia is a life-threatening condition in which body temperature falls well below the norm of 98.6oF.
However, because chilling causes normal body functions to slow down, doctors are exploring ways to use
hypothermia as a technique for extending time of delicate operations like brain surgery.
a.
The following table gives experimental data illustrating the relationship between body temperature and
brain activity.
Body Temperature (in oF) 50 59 68 77 86 98.6
Brain Activity (%normal) 11 16 24 37 52 100
b.
i.
Find an exponential regression to model the data.
ii.
Use the rule to estimate the level of brain activity at a body temperature of 39oF.
The next table gives experimental data illustrating the relationship between body temperature and safe
operating time for brain surgery.
Body Temperature (in oF)
50 59 68 77 86 98.6
Safe Operating Time (in minutes) 45 31 21 14 9 5
c.
i.
Find an exponential regression to model the data.
ii.
Write a Now-Next rule.
iii.
Use the rule to estimate the safe operating time at a body temperature of 39oF.
iv.
Find the body temperature at which safe operating time is predicted to be at least 25 minutes.
Cost is another important variable in medical practice. The next table gives data about charges for a
sample of routine surgeries, illustrating the relationship between time required for the operation and
hospital charges for use of the operating room.
Time (in minutes) 30 60
90
120
150
180
Cost (in $)
950 1,400 1,850 2,300 2,750 3,200
i.
Find a linear regression to model the data.
ii.
Use the rule to estimate the cost of an operation that takes 45 minutes.
iii.
Find the time of an operation for which cost is predicted to be $5,000.
2.
Deshauna invests $500 in a certain investment portfolio, which is expected to have a growth rate of at least 6%
per year.
a.
Write a function rule to model Deshauna’s balance.
b.
Write a Now-Next equation.
c.
How much money will she have in 7 years?
d.
If Deshauna does not invest any more money, how long will it take before he has at least $1,000 in her
account?
3.
If you invest $40 in an account for 10 years at a 3% interest rate how much money will you have?
4.
If you invest $50 in an account at a 2.5% interest rate, how long will it take for you to have $300 in the account?
5.
A population of 100 frogs increases at an annual rate of 22%. How many frogs will there be in 5 years?
6.
A type of bacteria doubles every hour. If there are 10 bacteria to start with…
a.
Write a NOW-NEXT rule to model the growth.
b.
Write a function rule to model the growth.
c.
Determine how many there will be in 5 hours.
7.
If you buy a used car for $9,000 and the value depreciates at 10% per year, determine the value after 4 years.
8.
Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each
round, half of the players are eliminated. How many players remain after 5 rounds?
9.
The population of Winnemucca, Nevada, can be modeled by 𝑃 = 6191(1.04)𝑡 where t is the number of years
since 1990.
a.
What was the population in 1990?
b.
Did the population increase or decrease each year?
c.
By what percent did the population change each year?
10.
An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by
about 29%. How much ibuprofen is left after 6 hours?
11.
For each of the following rules, decide whether the function represented is an example of:
o
o
Increasing Linear (IL)
Decreasing Linear (DL)
a.
𝑦 = 240(0.98)𝑥
b.
𝑦 = 9 + 3𝑥
c.
𝑦 = 35(5)𝑥
d.
𝑦 = 0.25(1.03)𝑥
e.
𝑦 = 68 − 2𝑥
f.
𝑦 = −25 + 10𝑥
2
o
o
Exponential Growth (EG)
Exponential Decay (ED)