Intercept Detectives
The y-intercept of the function y = 6(2)^x
What is (0, 6)?
This is the set of all possible x-values in a function.
What is the domain?
Find the domain of y = 3(2)^x.
What is all real numbers?
Write the equation
Initial value=3 Growth Factor=2
y=3(2)^x
population starts with 300 people and grows by 4% each year. Write a possible equation.
y = 300(1.04)^x
Find the y-intercept of y = 9(0.5)^x
What is (0, 9)?
This is the set of all possible y-values in a function.
What is the range?
Find the horizontal asymptote of y = 5(0.4)^x.
What is y = 0?
Write the equation
Initial value=10 Decay Factor=0.5
y=10(0.5)^x
A phone is worth $800 and loses 25% of its value each year. Write a possible equation
y = 800(0.75)^x
Find the y-intercept of y = 12(1.3)^x.
What is (0, 12)?
This is a line that a graph approaches but never touches.
What is an asymptote?
Find the range of y = 7(3)^x.
What is (0,\infty)?
Write the equation
Initial value=7 Growth Factor=1.2
y=7(1.2)
A bacteria culture starts with 150 bacteria and doubles every hour. Write a possible equation
y = 150(2)^x
What is the initial value of y = 15(0.8)^x?
What is 15?
This occurs when a quantity increases by a constant percent or multiplier over time
What is exponential growth?
State the domain, range, and asymptote of y = 2(5)^x.
Domain: All real numbers
Range: (0,\infty)
Asymptote: y = 0
Write the equation
Initial value=1 Growth Factor=5
y=1(5)^x
A lake has 2,000 fish and decreases by 10% each year. Write a possible equation.
y = 2000(0.9)^x
A function has a y-intercept of 20 and a growth factor of 3. Write a possible equation.
What is y = 20(3)^x?
This occurs when a quantity decreases by a constant percent or multiplier over time.
What is exponential decay?
A basic exponential function has a horizontal asymptote of y = 0. Its outputs are always positive. What is its range?
What is (0,\infty)?
A population starts at 50 and doubles each year
y=50(2)^x
A city has 5,000 people and grows by 2% each year. Write a possible equation.
y = 5000(1.02)^x