Growth vs. Decay
Growth or Decay?
y = 10(2/3)^x
Decay
The y-intercept of
y = 24(1.75)^x
(0, 24)
Write an equation:
"A population of penguins starts at 250 and increases by 2% each year."
y = 250(1.02)^t
x y
-1 2/3
0 2
1 6
y = 2(3)^x
General format for a "slope intercept" equation.
y = mx + b
Growth or Decay?
y = 0.8(2.6)^x
Growth
The domain and range of
y = 3(1/2)^x
D: all real numbers
R: y > 0
Find the % of change and identify it as growth or decay:
y = 1.5(0.72)^x
28% Decay
x y
1 125
2 25
3 5
y = 625(1/5)^x
Classify the polynomial by degree and by number of terms:
x^2 - 8x + 15
Quadratic Trinomial
x y
-2 32
-1 16
0 8
1 4
2 2
Decay
The asymptote of
y = 5(2)^(x - 3) + 4
y = 4
The amount in an account with an initial deposit of $2,500 and 3.7% interest compounded continuously after 20 years have passed.
$5,239.84
y = 1/8(4)^x
The name of the part of the quadratic formula that tells us how many and what type of solutions a quadratic equation has.
Discriminant
Growth or Decay?
y = 0.94(0.25)^-x
Growth
The domain and range of
y = -3(4)^x + 2
D: all real numbers
R: y < 2
The value of a $65,000 truck after 6 years given that it loses 1/5 of its value each year.
$17,039.36
Write an exponential equation that has a range of y < -3
Answers Vary
Example: y = -2^x - 3
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
Pascal's Triangle
The amount of an 80mg substance that remains after 108 hours if its half-life is 2 days.
16.82mg