Consider y = 2(1/3)^x. What is the initial value? What is the constant ratio?
What is a = 2, b = 1/3
100
Why is y = 6^x exponential growth?
What is because b > 1
100
Why is y = 2(1/4)^x exponential decay?
What is because 0 < b < 1
100
2^x = 32
What is x = 5
200
Simplify (y^10)/(y^6)
What is y^4
200
Consider the function y = 4^x. What is the initial value (a)? What is the constant ratio (b)?
What is a = 1, b = 4
200
What is the growth rate and growth factor of y = 100(1+0.25)^x ?
What is rate = 0.25 or 25%, factor = 1.25
200
What is the decay rate and the decay factor of y = 15(0.70)^x
What is rate = 0.30 or 30%, factor = 0.70
200
1/2 (10^x) = 50
What is x= 2
300
Simplify (x^2)/(x^8)
What is 1/x^4
300
Find the exponential function that passes through (0,1) and (1, 5)
What is y = 5^x
300
The population in a small town is 8,000 right now and is expected to double each year. Write an exponential function for this situation.
What is y = 8000(2)^x
300
Fish in a pond are dying out at a rate of 15% each day from pollution. There are 6,000 fish in the pond today. Write an exponential function for this situation.
What is y = 6000(0.85)^x
300
(1/6)^x = 1/216
What is x = 3
400
Simplify (x^3*y^4*z)^0
What is 1
400
Find the exponential function that passes through the points (0, 100) and (1, 10).
What is y = 100(1/10)^x
400
Kate buys a house for $225,000 and the value of it increases at a rate of 3% each year. Write an exponential function for this situation.
What is y = 225000(1.03)^x
400
John buys a new car for $32,000 but the value of the car depreciates at a rate of 6% each year. Write an exponential function for this situation.
What is y = 32000(0.94)^x
400
3^(x+1) = 9^(x-6)
What is x = 13
500
Simplify (x^5)^-2
What is 1/x^10
500
Find the exponential function that passes through the points (2, 8) and (3, 16)
What is y = 4(2)^x
500
You borrowed a 2 year, $10,000 loan. The interest rate on this loan is 7% and is compounded quarterly. How much money do you pay back?
What is $11,488.82
500
You invested $5,000 in stock that is losing its value at a rate of 5.2%. What will your investment be worth in 3 years? (Rounded to the nearest whole dollar).