2) Half-life problems can be modeled using the formula , where a is the

initial amount, k is the time it takes to reach the half-life, and t is the time. Make sure k

and t are using the same units!

Medicine has a half-life of 6 hours. Sally is given 600-mg of the medicine at 8AM.

a) What is the initial amount?

b) What is the time it takes to reach half the initial amount?

c) What is the formula to model this scenario?

d) How many mg of medicine will remain in her bloodstream after 24 hours?

Show all work. If you used a calculator, include screenshots.

3a-e (3 points per part) = 15 points total

3) Ronnie has $500 he wants to put in a savings account that compounds monthly at a

1% interest rate.

a) What is the initial amount?

b) What is the interest rate in decimal form?

c) What are the number of compounding periods in one year?

d) Write an equation that can be used to find the amount, A, after t years.

1+

0.01

12

12(t)

A=500

e)How long will it take for him to have $700 in his account?

b) Looking at the logarithmic form, does the 3 in correspond to x or y?

c) Looking at the logarithmic form, does (all of it) correspond to x or y?

d) To find the value of , find the 3 on the y-axis. Move horizontally until you hit

the function. Move vertically to determine the x-coordinate. This is the value of

. What is the approximate value of ? Round to the nearest tenth.

e) What is the approximate value of ?

5a-e (3 points per part) = 15 points total

5) Suppose you have the function .

a) What is the base of the log?

b) Complete the table using the given function, . Round to the nearest

unit.

1

10

100

1000

c) What is happening to the y values in the table in part b?

d) Are the x-values in the table in part b increasing by 10 or by a factor of 10?

e) Use part c and d to write a statement to describe the meaning of the base in the

function .

Solve the equations below. Check for extraneous solutions. Please show all work for

full credit.

log 2xlog 8=3

What logarithmic property did you use in

order to solve?

log(x+1)+log(x1)=log8

What logarithmic property did you use in

order to solve?