Section 2.1
Days: 0 10 20 30
Flu cases: 4 27 59 89
Which variable is the dependent variable?
Dependent Variable: 40 42 48 55 79 99
Fill in the blank:
This function is___________(increasing/decreasing)
The growth rate is ___________(positive/negative)
The growth rate is ________(increasing/decreasing)
This function is increasing
The growth rate is positive
The growth rate is increasing
This is an example of a function that is increasing at an increasing rate.
You joined a book club! Each month you pay $5 for the privilege of being in the book club plus $3 for every book you order. The cost of the book club is a function of the number of books ordered.
Is this function linear?
If so, find the following:
1) initial value (with unit)
2) growth rate (with unit)
3) formula
If you use letters in place of variables, please explain what they stand for.
Books ordered 0 1 2 3 4 5
Cost ($) 5 8 11 14 17 20
1) $5
2) $3 per book ordered
3) Cost = 3*books ordered + 5
If the following function is exponential, find its formula. If it is not exponential, explain why not.
A clan of gerbils starts with five and doubles every month.Let N = the number of gerbils and t = time in months
N = 5*2^t
Find the following without using your calculator:
log(100)
log(10,000,000)
log(10^89)
log(100) = 2
log(10,000,000) = 7
log(10^89) =89
Days: 0 10 20 30
Flu cases: 4 27 59 89
What is the percent increase in flu patients from day 0 to day 10? Write your answer as a percent.
What is the percent increase in flu patients from day 20 to day 30? Write your answer as a percent.
23/4 = 5.75 = 575%
The number of flu patients increased by 575% during that period.
89-59 =30
30/59 = .508 = 50.8%
The number of flu patients increased by 50.8% during this period.
The graph
1) goes up as we read from left to right
and
2) starts out "steepish" but ends up "flattish"
What type of graph does this describe?
The graph is _____________ at a(n) _________ rate.
Independent Variable (x) 0 3 6 9 12
Dependent Variable (y) -12 -18 -24 -30 -36
Is this function linear?
If so, find the formula.
YES. y = -2x-12
If the following function is exponential, find its formula. If it is not exponential, explain why not.
A population starts with 200 individuals and increases by 20% each year.
Let N = population and t = time in months.
N = 200*1.20^tAn Earthquake has magnitude 3.5. Find its relative intensity.
10^3.5 = 3162
Days: 0 10 20 30
Flu cases: 4 27 59 89
What is the average growth rate between day 0 and day 10. Interpret your answer by writing a complete sentence.
10-0 = 10
23/10 =2.3
Between days 0 and 10, the number of flu cases was increasing on average by 2.3 flu patients a day.
What should you do if you want to "deemphasize" change on your bar graph?
1) Use a wide range on the vertical axis.
2) Start your graph at zero.
The formula for a trend line is y = 5x +20
where
x is the number of math problems done per night in preparation for an exam
y is the score on the exam as a percent
Based on this formula, what score can you expect to have if you complete 10 math problems per night in preparation for your exam?
The balance of an investment is decreasing according to the rule: Next year's balance = .85 X this year's balance.
1) What is the constant percent decrease per year?
2) What is the base of the exponential function?
The base of the exponential function is .85.
How does the relative intensity of a magnitude 3 earthquake and a magnitude 5 earthquake compare?
The earthquake of magnitude 5 is 100 times greater than the earthquake of magnitude 3.
Days: 0 10 20 30
Flu cases: 4 27 59 89
How do you use extrapolation to estimate the number of flu cases on day 35?
89 + 5*average growth rate
89+ 5*3 = 104
A postage stamp cost $.06 in 1969. If the inflation rate from 1969 to 2018 is 575%, what is the cost of the postage stamp in 2018-dollars?
Step 1: 100% + 575% = 675%
Step 2: 676% of $.06 = $.41
So, the postage stamp that cost $.06 in 1969 would cost $.41 in 2018-dollars.
The formula for a trend line is y = 5x +20
where
x is the number of math problems done per night in preparation for an exam
y is the score on the exam as a percent
According to the formula, for every additional math problem you do, you can expect to increase your score on your exam by about _______
x 0 1 2 3
y 20 25 30 35
According to the formula, for every additional math problem you do, you can expect to increase your score on your exam by about 5%.
The balance of an investment is increasing according to the rule:
Next year’s balance = 3.15 × Current balance
1) What is the constant percent increase per year?
2) What is the base of the exponential function?
The base of the exponential function is 3.15.
800 = 400*(1.05^t)
2 = 1.05^t
2) Take log of both sides
log(2) = log(1.05^t)
3) Move the t to the front of the log
log(2) = tlog(1.05)
4) Divide both sides by log(1.05)
log(2)/log(1.05) = t.
t is approximately 14.
Days: 0 10 20 30
Flu cases: 4 27 59 89How do you use interpolation to estimate the number of flu cases on day 13?
27 + 3*average growth rate
average growth rate = 3.2 cases per day
So 27 + 3*3.2 = 37 flu cases
The graph
1) goes down as we read from left to right
and
2) starts out "flattish" but ends up "steepish"
What type of graph does this describe?
The graph is _____________ at a(n) _________ rate.
The graph to decreasing at an increasing rate.
A salesman makes $50 per week plus 10% of every sale! His weekly earnings is a function of his sales.
Is this a linear function?
If so, find the formula.
If you use letters in place of variables, please explain what they stand for.
Weekly sales 0 1 2 3
Earnings 50 50.10 50.20 50.30
Weekly earnings = .1s + 50
s = his sales each week in dollars.
Mathium-314 has a half-life of 40 days. Suppose we have an initial amount of 1,000 grams of mathium-314.
1) Find a formula for the amount of mathium-314 in terms of half-lifes.
2) Suppose 55 days have passed. How many half-lifes is that?
3) How many grams of mathium-314 are left after 55 days? Round your answer to the nearest gram.
Let h = the number of half-lives.
1) N = 1000*.5^h
2) Comparing Division: 55 days/40 days = 1.375 There are 1.375 half-lifes in 55 days.
3) N = 1000*.5^1.375 = 386 grams.
A radio is playing at 80 decibels.
A second AND third radio (both of which are also playing at 80 decibels) is turned on.
What is the combined decibel reading of the three radios? Round your answer to one decimal place.
Recall: Decibels = 10log(Relative Intensity) and Relative Intensity ≈ 1.26^Decibel
1 Radio:
Decibel reading = 80
Relative Intensity ≈ 1.26^80 OR 10^8
3 Radios:
Relative Intensity ≈ 3X1.26^80 OR 3X10^8
Decibel reading ≈ 10Xlog(3X1.26^80 ) = 85.1
OR 10log(3X10^8) = 84.8