Aim #80 : How do we write exponential equations?
Homework : Handout
Do Now : Multiple Choice: Which of the following statements is NOT true
regarding the exponential function y = 2
x
+ 4?
(1) The domain is all reals. (2) The average rate of change is constant.
(3) The y-intercept is (0,5). (4) The asymptote is y = 4.
In general exponential functions represent many real world applications of growth
and decay. To determine whether an explicit formula models exponential decay or
growth, we look at the value of the growth factor b. If b > 1, we have exponential
__________. If b < 1, we have exponential __________.
(This is true for formulas where our exponent is positive).
What happens to our output if the growth factor of the formula is 1?
A more specific form is the form where the growth rate "r" is input as a decimal
into the equation. "a" represents the amount you started with.
GROWTH : y = a(1 + r)
t
DECAY : y = a(1 - r)
t
Exponential Growth and Decay
y = a(b)
x
Identify the initial value, "a", in each formula below, and state whether the formula
models exponential growth or exponential decay. Justify your responses.
y = 300(1 + 0.2)
t
y = 75(1.25)
ty = 300(1 - 0.2)
t
y = 75(.75)
t
3-23-17
