Chapter 1
The x variable in this formula:
f(3)=32+1
What is 3?
N = 0.05t - 0.42t + 12.33
Here N is the enrollment in millions of students, t is the time in years since 1986, and the model is relevant from 1986 to 1996.
Use functional notation to express the number of students enrolled in U.S. public high schools in the year 1989, and then calculate that value.
What is 12.26?
From 2000 through 2014, the percentage of Americans living below the poverty level is given approximately by
P=11.36+0.28t
where t is the time, in years, since 2000.
According to this model, what percentage of Americans lived below the poverty level in 2010?
What is 14.16%?
In 2007, there were about 3.8 gigawatts of solar photovoltaic installations. From 2007 though 2014, the industry showed exponential growth, with a yearly growth factor of 1.45.
Make a exponential model that shows the photovoltaic installations, P, in gigawatts, at a time in t years after 2007.
What is 3.8 x 1.45t?
In the logistical formula:
E = 27,841.42 / 1 + 134.65e-0.646t
What is the variable called of 27,841.42?
What is K or carrying-capacity?
Calculate:
N(10) = 12.36/0.03+0.55t
What is 379.92
B = 1200 X 1.05t dollars
You want to buy a home entertainment center that costs $1500. How long will you need to wait to have enough money in your savings account? Round to nearest whole year.
What is 5 years?
4.1 7.7
5.7 8.3
7.3 8.4
8.9 8.9
10.5 9.1
What is y=0.2125+6.929?
In 2009, India consumed 20 exajoules of energy from all sources. It is anticipated that energy requirements for India will increase by 8% per year for the foreseeable future.
Make an exponential model for India that shows energy requirements E, in exajoules, t years after 2009.
What is E = 20(1.08t)?
In the logistical formula:
E = 27,841.42 / 1 + 134.65e-0.646t
What is the variable called of 134.65?
What is b?
The average rate of change from 0 to 5.
0 5.7
5 4.3
10 1.1
15 -3.6
20 -7.9
What is -0.28?
A potato is placed in a preheated oven to bake. Its temperature P=P(t) is given by
P = 400 - 325e-t/50, where P is measured in degrees Fahrenheit and t is the time in minutes since potato was placed in the oven.
Make a graph of P vs t.
Note: The potato should not be in the oven for more than a 2 hour period.
Calculate the initial temperature of the potato.
What is 75 degrees?
Suppose a drainage pipe slopes downward 6 inches for each 8-foot horizontal stretch. What is the slope of the pipe?
What is -6/8 or -0.75"?
0 32
1 25.60
2 20.48
3 16.38
4 13.11
Determine what type of data this table models.
What is exponential?
In the logistical formula:
E = 27,841.42 / 1 + 134.65e-0.646t
What is the variable called of -0.646?
What is r?
The 'Y' variable.
T(t) = 39.95 + 0.10 * t
What is 'T'?
Initially you have an inventory of 2000 sweaters on hand. You sell 400 sweaters each week.
Use s for the total number of sweaters remaining in inventory and w for the number of weeks, and find a formula that gives s as a function of w.
If you do not replenish your inventory, and if sales continue at this rate, how long will it be before your inventory is depleted?
What is 5 weeks?
8 120
11 165
14 210
17 255
What is the slope of this data?
What is 15?
N = Pat
Define the N
What is the end value?
N = K / 1 + be-rt
We can solve for r with the formula
r= ln(a)
Define a.
What is the growth rate factor?