Exponential and Logarithmic Functions Review

Writing and Exponential

100

Write the equation of an exponential function with an initial value of 2 and goes through the point (1,4)

N(x) = 2(2)^x

200

Image 1

y = 1(2)^x

300

Write the equation of an exponential that goes through the points (0,2) and (1,3)

N(x) = 2(3/2)^x

400

Image 4

N(x) = 1(2.45)^x

500

Write the equation of an exponential that goes through (0,2) and (3,1).

N(x) = 2(0.79)^x

Interest

100

We invest $2000 in a retirement account with 3% interest compounded annually. How much will we have in 20 years? 

A(t) = P(1+r/n)^nt

$3612.22

200

We invest 1000 dollars in an account that has 5.5% APR compounding quarterly.  How much will the account have in 25 years?

$3918.2

300

If you had an investment of $2000 earning 23% per year compounding continuously, how much would you have after 3 years?

About $3987.43

400

You want to put a down payment on an apartment in 8 years which would cost $20,000.  If you invest now in an account that has 3% APR compounding daily, how much would you need to invest?

$15732.712

500

In 40 years you would like to retire with $100,000.  If you invest $5,000 in an account that compounds quarterly, what is the smallest APR your account can have? To the nearest hundredth.

Approximately 0.0756 which is roughly 7.6%.

Solving using Exponentials and Logs

100

Solve for x by converting the log to exponential form: log_1/2(x) = 3

0.125

200

Solve for x using a log: 2^x+2=24

About 2.585

300

Solve for x: log(2x+4)-log(2) = 1

8

400

Rewrite 15^2x-3=1000 as a log. Then apply change of base with natural log to solve for x. 

About 3.775

500

Use logs to find the exact solution to -5e^-x-9-7=-32

About -10.609

Transformations

100

What transformation has happened to this exponential? 

(3)^x-2

Right 2

200

What two transformations have happened? -2(3)^x

Vertical Stretch by 2 and reflect over x axis

300

List all transformations of the equation: 

2log₃(x-3)+4

Vertical stretch 2

Right 3

Up 4

400

List ALL transformations that have occurred: 

-1/3log₄(x+5)+6

Vertical Compression 1/3

Left 5

Up 6

Reflect over x axis

500

List ALL transformations: -1/2(2)^(-x-3)-7

Vertical Compression 1/2

Right 3

Down 7

Reflect over both axis

Misc.

100

f(x) = 2(3)^x  What is f(2)

18

200

Population of a group of seals started at 6.  Their groups is growing at a rate of 19% per year. After 20 years, how many seals will there be/ (assuming none die).  f(x) = 6(1.19)^x

Roughly 194 or 195 seals

300

Rewrite log_t(32) - log_t(4) in compact form. (Fully Simplify)

log_t(8)

400

You want to put a down payment on an apartment in 8 years which would cost $20,000.  If you invest now in an account that has 3% APR compounding daily, how much would you need to invest?

$15732.712

500

A mineral decays at a continuous rate of 12.3% per day.  How much will 5000g decay to in 2 weeks?

About 893.54 grams