Exponential Functions
A town has a population of 141,300 and grows at a rate of 5% every year. What is the equation that represents the town’s population after 6 years?
P=141,300(1+0.05)^6
What is the slope of the line that passes through the points (−5,6) and (−9,−6)? Write your answer in simplest form.
3
Skylar is a salesperson who sells computers at an electronics store. She makes a base pay of $100 each day and is also paid a commission for each sale she makes. One day, Skylar sold 8 computers and was paid a total of $120. Write an equation for P, in terms of x, representing Skylar's total pay on a day on which she sells x computers.
P = 2.50x +100
Solve for x:
8x − 9 = 5x + 9
x = 6
What is the x-intercept and y-intercept of the following equation?
10x +2y = 10
y-intercept: (0,5)
x-intercept: (1,0)
Logan has a collection of vintage action figures that is worth $400. If the collection appreciates at a rate of 4% per year, what is the equation that represents the value of the collection after 6 years?
V=400(1.04)6^6
The table below represents a linear function. Identify the rate of change of the function.
x : -4, -2, 0, 2
y: -1, 0, 1, 2
1/2
Chee just lit a new candle and then let it burn all the way down to nothing. The candle burned at a rate of 0.5 inches per hour and after burning for 10 hours, the candle's height was down to 3 inches. Write an equation for L, in terms of t, representing the length of the candle remaining unburned, in inches, t hours after the candle was lit.
L = −0.5t +8
Find the solution of the system of equations.
−6x + 3y=−15
4x − 3y= 13
( , )
(1 , 3)
Identify the root(s) of the following equation:
−3x + 5y = 15
-5 or 15/-3
A radioactive compound with mass 480 grams decays at a rate of 15.1% per hour. What equation represents how many grams of the compound will remain after 2 hours?
C=480(1−0.151)(1−0.151)
What is the rate of change of the function y = 5x + 4?
5
Tallulah is moving and must rent a truck. There is an initial charge of $35 for the rental plus a fee of $2 per mile driven. Write an equation for C, in terms of m, representing the total cost of renting the truck if Tallulah were to drive m miles.
C = 2m + 35
Solve the system by substitution.
y = 9x
y = 8x + 4
( , )
(4 , 36)
What is the solution of the following equation?
4x − 3y = 12
3
8,900 dollars is placed in a savings account with an annual interest rate of 3.3%. If no money is added or removed from the account, what equation represents how much will be in the account after 4 years?
M=8,900 (1.033) (1.033) (1.033) (1.033)
The satellite Space Explorer flies 9800 miles in 7 hours. Find the rate of change.
9800 miles / 7 hours
1400 miles per hour
Khadija is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The daily fixed costs are $600 and and the total cost of producing 4 phones in a day would be $900. Write an equation for C, in terms of p, representing total cost, in dollars, of producing p phones in a given day.
C = 75p + 600
Does the following set of ordered pairs represents a function?
{(−1,−3),(−7,−5),(3,5),(−2,−3)}
YES
Find the zero(s) of the following equation:
3x + 6y = 12
4
A new car is purchased for 21,100 dollars. The value of the car depreciates at a rate of 2% per year. What equation represents the value of the car after 5 years?
V = 21,100 (1−0.02) 5^5
A health club charges a one-time sign-up fee and a monthly membership fee. The equation y = 28x + 50 represents what the health club charges. Find the rate of change.
$28 per month
Eva is a salesperson who sells computers at an electronics store. She is paid a $2.50 commission for every computer sale she makes and she also makes a guaranteed base pay of $55 each day. Write an equation for P, in terms of x, representing Eva's total pay on a day on which she sells x computers.
P = 2.50x + 55
Given f(x)=−4x − 5, find f(−4).
11
Solve the following equation:
−10x + 8y = 40
x = -4
y = 5