EXPONENTIAL RULES
RADICALS & RATIONALS
EXPONENTIAL FUNCTIONS
SEQUENCE
FINAL JEOPARDY
100
SOLVE.
3^5*3^4
3^9
100
IS THIS RADICAL OR RATIONAL?
(sqrt(8))^5
RADICAL
100
IS THIS EXPONENTIAL OR LINEAR?
EXPONENTIAL
100
IS THIS SEQUENCE ARITHMETIC, GEOMETRIC OR NEITHER?
2, 4, 6, 8, 10
ARITHMETIC
250
SOLVE.
4^3/4^5
4^-2
1/16
250
CONVERT INTO A RATIONAL
(sqrt(8))^9
(8)^(9/2)
250
EXPONENTIAL DECAY OR EXPONENTIAL GROWTH?
EXPONENTIAL DECAY
250
IS THIS SEQUENCE ARITHMETIC, GEOMETRIC OR NEITHER?
1/4, 2, 16, 128, 1024
GEOMETRIC
500
DOUBLE JEOPARDY!!!(5 POINT MINIMUM BID)
SOLVE.
(z^12*z^3)/z^6
z^9
500
CONVERT TO A RADICAL
17^(1/2)
sqrt(17)
500
SOLVE.
2^(2x) = 2^(x-2)
x=-2
500
WHAT IS THE COMMON RATIO?
4/9, 4, 36, 324
r = 9
750
SOLVE.
(10x^3y^0)^3
1000x^9
10^3x^9
750
DOUBLE JEOPARDY!!! (5 POINT MINIMUM BID)
CONVERT TO A RATIONAL
(sqrt(10x))^7
(10x)^(7/2)
750
WHAT IS THE SOLUTION FOR THIS EXPONENTIAL EQUATION?(DESMOS ALLOWED)
256^(x+2) = 16^(3x-1)
x = 5
750
WHAT IS THE COMMON RATIO?
1, 5, 10, 15, 25
NO COMMON RATIO
1000
JEOPARDY SWAP!!! (SOLVE FOR YOURSELF AND GET 1000 POINTS. OR CHOOSE ANOTHER TEAM TO ANSWER IT. IF THEY GET IT WRONG, YOU EARN 2000 POINTS. BUT IF THEY GET IT RIGHT, THEY GET 1500 POINTS.)
SOLVE.
(b^3n^-3m^10)/(b^-4n^-5m^4
b^7n^2m^6
1000
SIMPLIFY. CHANGE FROM RADICAL TO RATIONAL
sqrt(x^4y^0z)
x^2(z)^(1/2)
1000
A company promises to release a new smartphone model every month. Each model's battery life will be 3% longer than the previous model's. Write the formula for this exponential function. If the current model's battery life is 726.0 minutes, what will the latest model's battery life be 5 months from now?
726(1.03)^5
The battery life will be 841.6 minutes
1000
JEOPARDY SWAP!!! (SOLVE FOR YOURSELF AND GET 1000 POINTS. OR CHOOSE ANOTHER TEAM TO ANSWER IT. IF THEY GET IT WRONG, YOU EARN 2000 POINTS. BUT IF THEY GET IT RIGHT, THEY GET 1500 POINTS.)
Solve for the a10 term of the geometric sequence:
-2, 10, -50, 250...
= -2(-5)^(n-1)
-2(-5)^((10)-1)
-2(-5)^9
=3906250
2000
FINAL JEOPARDY (0 MINIMUM. ALL POINTS MAXIMUM)
Is the sequence shown an arithmetic sequence? a geometric sequence? Explain your reasoning.
3, 3, 3, 3, . . .
ANSWER:
ARITHMETIC SEQUENCE: YES;
It is an arithmetic sequence with a common difference of 0.
GEOMETRIC SEQUENCE: YES;
It is a geometric sequence with a common ratio of 1.