Key Features Expon. f(x)'s
Growth or Decay
Word Problems
Compound/Simple Interest
100
If, y = a(bx), What are the parameters (a & b) and what do they represent?
a = initial amount/y-intercept
b = factor
100
How do I know if an exponential function is exponential decay from an equation?
If the b is in between 0 and 1
100
2243
100
How much money would one have in total if they put $34,000 into a savings account with a 4% interest rate for 3 years?
$38,080
200
f(x)=37(1.07)x
Does this function represent exponential growth or decay? What's the factor?
Exponential Growth.
Factor: 1.07
200
Does the graph represent exponential growth or decay?
Exponential Growth
200
What will be the cost in 17 years?
$32,313.27
200
The total value accumulated if you start off with $7,300 at 0.7% interest rate compounded daily for 10 years.
$7,829.30
300
What is the y-intercept and horizontal asymptote?
y-intercept = (0, 1)
asymptote (boundary): y=0
300
f(x)=a(.93)x
Does this functions represent exponential growth or decay? What is the r value?
Exponential Decay
r = 7% or .07
300
16,941 people
300
If Ellie invests $40,000 into an account that is continuously compounded with an interest rate of 2.6%, how much money will she have accumulated after 14 years?
$57,563
400
What are two guaranteed points on the graph of y=4(2)x?
(0,4) and (1,8)
(remember, when x=0, y=a; when x=1, y= a(b) )
400
Ms. Wiggins purchased a car for 26,400 and every year it decays by 12%. What can she expect the value of her car to be after 3.5 years?
f(x)=26400(.88)3.5=$16,876.92
400
A video on a platform starts with 2,000 views and grows to 16,000 views in 4 days. What is the daily growth rate of views?
Roughly 68% Increase
400
Total amount in the bank if you started off with $18,000 at 9% interest rate compounded weekly for 6 years.
$30,825.95
500
Label the following formula:
y = final amount
a = initial amount
r = rate of growth
t = time
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
You put $500.00 into an account that earns 3% interest annually. If you do not deposit any other money into the account, how many years will it take for your account to be over $750?
500(1+.03)14=756.29
It will take 14 years for the account to be over $750.
500
Suppose you are trying to pick a savings account to deposit $5,000. Which option is better and why?
Option A: 14.5% interest rate compounded daily for 4 years
Option B: 17% interest rate compounded semiannually for 4 years
How much money will you earn with the better option?
Option B