Jeopardy-Unit 5: Exponential Functions Review–ITF

Simplify

100

[3n²(5⁰)]/(2n³)

3/(2n)

200

(2x^-5y³n⁴)/(4n²y^-12)

(y¹⁵n²)/(2x⁵)

300

[(4x^-3y²)/(6x⁵)]*[(9x²y³)/(x^-2y^-1)]

(6y⁶)/x⁴

400

(a^-4b²c²d¹⁵)/(5^-2a¹⁰b^-5cd^-4)

(25b⁷cd¹⁹)/a¹⁴

500

[(-2f^-4g³h)/(3f⁶g^-6h³)]^-3*[(g⁸⁴h^-2)/(f^-6gh^-3)]

-(27g⁵⁶f³⁶h⁷)/8

Graphs

100

Fill out the points of y=2^x on a table. (x-points are -2, -1, 0, 1, 2)

(-2,1/4)

(-1,1/2)

(0,1)

(1,2)

(2,4)

200

Fill out the points for the equation 5(.5)^x on a table. (-2, -1, 0, 1, 2)

(-2, 20)

(-1, 10)

(0,5)

(1, 2.5)

(2, 1.25)

300

(-2, 16)

(-1, 8)

(0, 4)

(1, 2)

(2, 1)

What is the equation matching these points?

f(x)=4(.5)^x

400

Compare the function to its parent function and tell if the equation is a stretch or a compression of the parent function, translated up, down, left, or right, reflection or not, domain and range, equation for horizontal asymptote, and y-intercept.

y=-5(2)^x-1-2

Stretch, reflection, translation right and down, D=All real numbers, range– y<-2, asymptote– y=-2, y-int=-4.5

500

Compare the function to its parent function and tell if the equation is a stretch or a compression of the parent function, translated up, down, left, or right, reflection or not, domain and range, equation for horizontal asymptote, and y-intercept.

y=0.1(0.5)^x+1+2

Compression, not reflection, translation left and up, D=All Real Numbers, R– y>2, Asymptote– y=2, y-int=2.05

Growth and Decay

100

Find a bank account balance if the account starts with $100, has an annual rate of 4%, and the money left in the account for 12 years. Write equation and then solve.

y=100(1.04)^x, y=$160.10

200

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011? Write equation and solve.

y=30,000(1.05)^x, x=51, y=361,223,09

300

You deposit $1500 into an account that pays 6% annual interest compounded quarterly. Find the balance in the account to the nearest cent after 3 years and 10 years. Find equation and solve.

y=1500(1+0.06/4)^4x, 3 years: $1,793.43, 10 years: $2,721.03.

400

DAILY DOUBLE!!!!!!!!!

WAGER??? _________

What is the y-intercept of the equation y=2^x?

Mrs. Raditz, you answer this one.

500

The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay half of the initial amount. The half-life of the radioactive gas radon is approximately 3.8 days. The initial amount of radon used in an experiment is 75 grams. If N represents the number of grams of radon remaining t days after the start of the experiment, write an equation that gives N in terms of t.

N(t)=75(0.5)t/3.8

Radical Exponents

100

Write a^1/4b^5/8 with a single radical.

8th root of a²b⁵

200

Simplify (-32)^4/5

16

300

Simplify (3x^1/2)(4x^2/3)

12x^7/6

400

Solve for x:

(4^1/5)^x=64

x=15

500

Simplify -8^2/3x^2/3x^1/2y^1/3

-4x times 6th root of xy²

Miscellaneous

100

A diamond ring was purchased twenty years ago for $500. The value of the ring increased by 8% each year. What is the value of the ring today? 

V=500(1.08)²⁰=$2330.48

200

FINAL JEOPARDY! EVERYONE WAGER!

_________

_________

_________

_________

_________

_________

In the equation y=(2)^x-7+3, is the original equation stretched or compressed?

Ask Mrs. Raditz for the answer.

300

Well guess what, you lost your turn! 

;)

400

In 2000, you bought a car. In 2003, it is worth $15000. In 2010, it is now worth $6000. Assuming that the car's value decays exponentially with a horizontal asymptote of 0, write a model for the situation. What will be the value of the car in 2020? (Remember: Use your calculator!)

y=22,214.52(0.877)^x, 2020-$1609.27

500

My mom decides to give me an allowance. On day 1, she gives me 2 pennies. The next day, she doubles the amount of money she gave me the day before. How much money do I have on day 20?

$20.971.50!!!