Key Features Expon. f(x)'s
Growth or Decay
Growth or Decay
Word Problems
Solving
100
If, y=a(bx ), What do a and b represent?
a=initial amount/y-intercept
b=multiplier for each y
100
f(x)=3(.93)x
Does this functions represent exponential growth or decay?
Exponential Decay
100
A bunny population doubles every 6 months. If the starting population is 10. What is the initial population? What is the growth factor?
initial population = 10
growth rate = 2
100
2243
100
4x+3=42x
x=?
x = 3
200
Which number is the y-intercept and which is the multiplier for the function f(x)=2(3)x
y-intercept=2
multiplier= 3
200
Find the exponential equation for:
Passes through the points (0, 3.5) and (1, 14)
y=3.5(4)x
200
In exponential functions, when a> 0 and b>1, will this be exponential growth or decay?
Exponential growth
200
What will be the cost in 17 years?
$32,313.27
200
24=4x+1
x=?
x = 1
300
What is the equation for the graph below?
y = 1(2)^x
300
How do I know if an exponential function is exponential growth or decay from an equation?
Check: if a is greater/less than 0
if b is greater/less than 1
If both inequality signs (< or >) are the same, then GROWTH
300
f(x)= - 4(1.07)x
Does this functions represent exponential growth or decay? What's the constant percent rate of change?
Exponential Decay
107%.
300
16,941 people
300
32x=27x+1
x=?
x= -1
400
What is the multiplier or b for this table?
b=2
400
What is the growth factor in y= abx
b (as a %) so b X 100
400
Does this graph show exponential growth or decay?
Exponential Growth
400
A $12,000 deposit into a bank account will earn 3% annual interest compounded continuously. How much will be in the account after 10 years?
$16,198.31
400
125=52x-1
x=?
x=2
500
Linear functions have a constant ________ and Exponential functions have constant ______ between consecutive outputs.
Linear has a constant difference between each y-value (add or subtract a number)
Exponential has a constant ratio (or multiplier) between each y-value
500
Ms. Wiggins purchased a car for $26,400 and every year the value of the car depreciates by 12%. How much will the car be worth after after 4 years? SHOW THE FORMULA YOU USED TO GET YOUR ANSWER.
f(x)=26400(1 - 0.12)4 = $15,831.96
500
Annual sales of a fast food restaurant are $530,000 and increasing at a rate of 5%. What will the annual sales be in 6 years?
530,000(1.05)6 =$710,250.69
500
If you put $500.00 into an account and the account earns 3% interest, compounded quarterly. How much will be in the account after 5 years?
$580.59
500
4x+1=82x
x = 1/2