Reagents Review

Half Life Equations

100

If a material has a half life of 4 days and an initial amount of 400mg, how many mg will there be after 4 days?

200mg

200

If a medicine has a half-life of 7 hours and has an initial dosage of 350mg, how many mg will there be after 14 hours?

87.5

300

Write an equation for the amount of medicine left in your body M(t) if it has a half-life of 2 hours and an initial dosage of 400mg. 

M(t)=400(0.5)^t/2

400

Write an equation for the amount of material left in the form A(t) = A_oe^-rt where A_o is the initial amount (400mg) and r is the decay rate (0.442) in terms of.

A(t) = 400e^-0.442t

Exponential Equations

100

Solve for x:

4^x = 4^3x+1

x = -1/2

200

Solve for x:

6^x-1 = 36^x+2

x = -5

300

Solve for x:

4*3^x-1 = 14

x=2.14

400

Solve for t:

300 = 200e^t/4

t=1.62

Finding Inverses

100

What is the inverse of y=log₂x

f^-1(x) = 2^x

200

What is the inverse of y = 4^x

f^-1(x) = log₄x

300

Is the point (1,4) a point on the inverse of y=2^x?

No, inverse is y=log₂x

400

is the point is the point (2,25) a point on the inverse of the function f(x)=log₅x

Yes it is. Inverse is f^-1(x) = 5^x

Sequences and Sums

100

The explicit definition of a sequence is given as:

f(n) = 7 + 0.25n where n is the term number. What is the 10th term in the sequence?

9.5

200

Write the explicit equation for the following sequence:

6, 2, -2, -6, -10 .....

f(n) = 6-4(n-1)

300

Use your notes and write the equation for the amount of money in an account B(t) if the initial investment is $250 compounded 4 times a year at a 3.4% interest rate after t years.

B(t) = 250(1+(0.034/4))^4t

400

A book drive initially has 40 books in it. If the number of books increases by 20% every hour, write a summation equation that gives the number of books in the drive after 4 hours.

See Mr. Waggoner's notes.

Misc

100

What is the solution to the following quadratic:

y = 3x²-5x+3

x = (5±11i)/6

200

What interval has the greatest rate of change (see power point)

[-2,-1]

300

Sketch f(x) and f(x) - 3 on your board. f(x) given in powerpoint slides.