Growth or Decay?
is the function f(x)=2^x exponential growth or decay?
Growth
What is the y-intercept of f(x) = 2^x?
(0,1)
Exponential functions are often used to model what kind of situations?
Population growth, radioactive decay, interest, and epidemics.
Solve: 2^x = 8
x = 3
is f(x) = 0.5^x growth or decay?
Decay
True or False: The graph of any exponential function passes through (1,a) where a is the base.
True
If a population triples every 10 years, is that exponential growth or decay?
Growth
Solve: 3^x = 81
x = 4
What does the base of an exponential function tell you about growth or decay?
If the base is greater than 1, it's growth; if it's between 0 and 1, it's decay.
Sketch the graph of f(x) = 3^-x. Is it growth or decay?
Decay, reflected over the y-axis.
You invest $1,000 annual interest, compounded yearly. Write the exponential equation.
A(t) = 1000(1.05)^t
Solve: 5^(x+1) = 125
x = 2
Identify the type of function: f(x) = 7(0.89)^x
Decay
Describe the transformation from f(x) = 2^x to f(x) = 2^(x-3) + 4.
Right 3 units, up 4 units.
A substance decays at a rate of 12% per year. What is the decay factor?
0.88
Solve: 4^x = 1/64
x = -3
Which of the following is NOT exponential growth?
a) f(x) = 3^x
b) f(x) = 1.01^x
c) f(x) = 0.97^x
d) f(x) = 5e^x
c) f(x) = 0.97^x
What is the horizontal asymptote of f(x) = -4(1.5)^x +2?
y = 2
A bacteria culture doubles every 3 hours. If it starts with 50 cells, how many after 9 hours?
50 x 2^3 = 400
Solve: 2^x = 7
x = log2(7)