Exponentials & Logarithms

Exponential Functions

100

What type of exponential function is h(x)?

h(x)=4^x

Increase

200

What type of exponential function is h(x)?

h(x)=(1/3)^x

Decrease

300

If you were to sketch y= 5^x-2+3, where would the asymptote be located?

x=3

400

Newly planted seedlings approximately double their weight every week. If a seedling weighing 5 grams is planted at time t=0 weeks, which equation best describes its weight, W , during the first few weeks of its life?

W= 5*2^t

500

Mark is using two functions to determine how much money he will have in his account after  years.  He uses the constant function f(t)=2500 and an exponential function g(t)=1.05^t to create the function h(t)=f*g. What is the value of the account after 8 years?

$3694

Evaluating Exponential Expressions

100

Evaluate k(0).

g(x)=3^x

1

200

Evaluate g(2).

g(x)=2^x+1+4

12

300

Sabena invests $250 in an account that earns 2.4% interest per year compounded continuously.  How many years will it take the account to have a value of $300?  Round your answer to the nearest tenth.

7.6 years

400

Nathan has just bought a new car.  He models the value, V, in dollars, of the car after t years as V(t)=21,000(0.861)^t. By what percent does the value of Nathan's car decrease each year?

13.9%

500

Solve for x.

18=2(3)^x+3

x=-1

Logarithmic Functions

100

What line does the exponential reflect across to create a logarithmic function?

y=x

200

Evaluate log₅5⁹

9

300

What type of transformation does log₃(x-1) have?

Shifts to the right by 1 unit

400

Describe as many methods as you can to solve the equation 3^x= 12. Which do you prefer? Why?

logarithms, guess and check, graphically

500

What does log₂0 equal? Explain why.

It is undefined. There is no number we can raise 2 to in order to get 0.

Evaluating Log Expressions

100

Evaluate log₆36

2

200

Using Desmos, calculate the value of log₂75

6.2288186905

300

If log₄(x)=-2, what is the value of x?

x=1/16

400

Find and equivalent expression to logx+logy-logz.

log(xy/z)

log(xy)-logz

log(x)+log(y/z)

500

Evaluate 6^log₆216

216

Miscellaneous

100

Solve 2x²+5x=4x²-12

x= -3/2 and 4

200

Are the following two expressions equivalent?

3(x-2)²+6 and 3x²+18

Not Equivalent

300

Given g(x)= -3x+1, what does g (a+1) equal to?

-3a+2

400

What is the inverse function for f(x)=3x²-4?

y=sqrt (x+4/3)

500

If f(x)=2x² and g(x)=3x-5, calculate f(g(3))

f(g(3))=32