Linear Functions
Exponential functions
Applications of functions to economics
Power functions and proportionality
100

How do you find slope?

(y2-y1)/(x2-x1)

100

Find the equation of the exponential function that passes through the points (2, 12) and (7, 36)

y=7.732 * (1.246)x

100

Suppose the radio company sells their radios for $15 each 


Model the revenue that the radio company makes

R(q)=15q

100

y is directly proportional to x, and when x=3 then y=15.
What is the constant of proportionality?

k=5

200

Find an equation of the line that passes through the points (4,3) and (1,8)

What is -5/3x + 29/3?

200

A bacteria doubles in 12 hours.

Find its annual growth rate

Find its continuous growth rate 

What is r=.059? what is k= (ln(2)/12)?

200

R(q)= 15q

C(q)= 24000 +7q


FIND THE BREAK EVEN POINT 

15q=24000+7q

q=3000

200

  1. Which of the following are power functions? 

  1. 5/x^3 

  1. 5 * 2^x

  1. 2/3x 

  1. 3x^½

What is ALL OF THEM ARE POWER FUNCTIONS EXCEPT 

5 * 2^x?

300

The pollution level in the centre of a city at 6 am is 30 parts per million and it grows in linear fashion by 25 parts per million every hour. If y is pollution and t is time in hours after 6 am, determine:

1.The equation that relates y with t.

2. The pollution level at 4 o'clock in the afternoon.

1.The equation that relates y with t.

y = 30 + 25t

2. The pollution level at 4 o'clock in the afternoon.

10 hours have elapsed between 6 in the morning to four in the afternoon.

f(10) = 30 + 25 · 10 = 280

300

When a patient is given to the antibiotic ampicillin, it is metabolized and eliminated from the bloodstream at a rate of about 40% per hour. A typical dose is 250 mg. Let Q=f(t) be the amount of ampicillin left in the body t hours after 250 mg of the drug was administered. Model the amount of the drug left in the bloodstream using an exponential decay model.

Q= Qo*at

Q=250(.6)t


r=-0.4

a= 1+r

300

A movie theater has fixed costs of $5000 per day and variable costs averaging $6 per customer. The theater charges $11 per ticket. How many tickets per day does the theater need to sell in order to make a profit?

5000 + 6C = 11C

1001 Tickets per day to make a profit

300

Circulation time of a mammal is proportional to the FIFTH root of the body mass of the mammal. 

  1. Write the formula for the circulation time, T, in terms of body mass, B. 

  1. If the elephant has a body mass of 6000 kg has a circulation time of 200 s, find constant of proportionality

1. T= B1/5k

2. k= 35.11 

400

The base a form of Poe0.14t  is ?

P0(1.15)t

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