Exponential Function Characteristics
Does the following function show exponential growth or decay?
f(x)=427(0.82)x
Decay
Note: Decay Factor is 82%, while the Decay Rate is 18%
Which function has a higher starting value?
p(x)=10(4)x OR q(x)=40(2)x
q(x)
Solve y=24
y=16
What kind of functions are modeled by simple interest investment accounts? (function family)
Linear functions
What kind of functions are modeled by compound interest investment accounts? (function family)
Exponential functions
What is the y-intercept of the function f(x)=1620(2.4)x ?
**Remember to use proper notation**
(0,1620)
Name two characteristics that all four of these functions have in common.
f(x)=200(0.25)x
g(x)=200(0.5)x
h(x)=200(0.75)x
j(x)=200(0.875)x
Acceptable answers:
Domain, range, asymptote, y-intercept, they're all decay functions, all exponential
Solve 3x=81
x=4
Which investment will have more money added each year?
Investment A desposited $500 at 2% interest
Investment B deposited $500 at 12% interest
Investment B ($60 vs $12 per year)
Which compounding interval is compound more times in one year? Quarterly or Semi-Annually
Quarterly (4x/yr)
What is the growth RATE of the function f(x)=200(1.75)x?
0.75 (or 75%)
Which function is decaying more quickly?
f(x)=1000(0.1)x OR g(x)=1000(0.9)x
f(x)
What is x when 3=1.5(2)x?
x=1
Which investment has the lowest return (money added to the account) each year?
Investment 1 of $100 at 5% simple interest
Investment 2 of $400 at 5% simple interest
Investment 3 of $200 at 10% simple interest
Investment 1
How many times is an account compounded in a 4-year period if it is compounded semi-annually?
8 times (twice per year for four years)
What is the y-intercept of the function f(x)=5(2)x+1?
**Remember to use proper notation**
(0,6)
Which function is modeled by the red line A?
https://docs.google.com/presentation/d/1rWZIADt5Dht_AwVKC2cVhuGNBg0zys-cmpF-_n0VRdQ/edit?usp=sharing
q(x)
Solve for x when 160=20(2)x
x=3
How much money is added to an investment account each year if $400 was initially deposited at 16% simple interest rate?
$64 per year
Find the missing value:
https://docs.google.com/presentation/d/1rWZIADt5Dht_AwVKC2cVhuGNBg0zys-cmpF-_n0VRdQ/edit?usp=sharing
503.88
432/400=1.08 (growth factor), so 466.56*1.08=503.88
What is the range of the function f(x)=2(1.5)x?
(You may use interval notation, set notation, or describe the range in a statement.)
y>0
(0,infinity)
If the red function has a growth factor of 3, how does the growth factor of the blue function compare to 3? (bigger, smaller, equal to?)
https://docs.google.com/presentation/d/1rWZIADt5Dht_AwVKC2cVhuGNBg0zys-cmpF-_n0VRdQ/edit?usp=sharing
Smaller because it is a slower curve and therefore has slower growth
Jada saw a music video that her favorite singer posted online. The equation v(t)=320(4)t represents the number of views v of the video, t days since Jada saw the video. After how many days did the artist have 20,480 views?
3 days
How much money is added to a bank account over a 4-year period if the initial deposit was $500, and it carried a simple interest rate of 10%?
$200
What is the growth FACTOR of an investment account that is compounded monthly at a 15% interest rate?
1.0125
(1+0.15/12)