Exponential Function

Exponential Functions

100

Given y = 2(3)^x, determine the y-intercept.

(0, 2)

200

Given y = 5(1/2)^x, determine the y-intercept.

(0, 5)

300

Given the coordinates (0, 2) and (1, 6), determine the b-value of the exponential function (of the y = a(b)^x)

b = 3

400

Given the coordinates (0, 4) and (3, 32), determine the a- and b-values of the exponential function (of the y = a(b)^x)

a = 4 and b = 2

500

Given the coordinates (2, 3) and (4, 27), determine the b-value of the exponential function (of the y = a(b)^x)

y = (1/3)3^x

Exponential Growth or Decay

100

Determine if the exponential function represents growth or decay:

y = 2(3)^x

Growth

200

Determine if the following represents growth or decay:

y = 5 (0.45)^x

Decay

300

Determine if the following represents growth or decay:

y = 2(0.75)^-x

Growth!

400

Determine the rate of growth or decay given

y = 2(1.6)x

0.6 rate of growth

500

Determine the rate of growth or decay given

y = 7(0.85)x

0.15 rate of decay

mult. exponents

100

rewrite using positive exponents

7^3•7^10

7^13

200

rewrite using positive exponents

11^7•11^24

11^31

300

Evaluate

(2/4)^2

1/4 or 4/16

400

rewrite using positive exponents

4/5•4/5•4/5•4/5•4/5

(4/5)^5

500

rewrite using positive exponents

(2^4 )^5

2^20

div. exponents

100

rewrite using positive exponents

4^8/4^3 

4^5

200

rewrite using positive exponents

12^11/12^7 

12^4

300

rewrite using positive exponents

(9^6•9^9)/9^11 

9^4

400

rewrite using positive exponents

(3/4)^25/(3/4)^20 

(3/4)^5

500

rewrite using positive exponents

s^17/s^11 

s^6

variables w/ exponents

100

rewrite using positive exponents

p^13/P^11 

p^2

200

rewrite using positive exponents

(x^12•2^2)/x^9 

4 x^3

300

rewrite

x^2/x^2 

1

400

rewrite using positive exponents

n^10/m^5 •m^12/n^7 

n^3*m^7

500

rewrite using exponents

6v^2•6v^2

36v^4

Negative exponents

100

rewrite using positive exponents

5^-7

1/5^7

200

evaluate

3^-4

1/81

300

rewrite

7^0

1

400

rewrite using positive exponents

7^(-9)/7^3 

1/7^12

500

rewrite using positive exponents

11^(-3)/11^4 

1/11

Common Bases

100

125 = 5^x

x = 3

200

Solve for x:

8^x = 32

5/3

300

3^x-7 = 27

x = 10

400

4^2x+3 = 4³

x = 0

500

5 ^{x + 6} = 125 ^{x - 4}

x = 9