Half Life Equations

Exponential Equations

Finding Inverses

Sequences and Sums

Misc

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

Solve for x:

4^{x} = 4^{3x+1}

x = -1/2

What is the inverse of y=log_{2}x

f^{-1}(x) = 2^{x}

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

What is the solution to the following quadratic:

y = 3x^{2}-5x+3

x = (5±11i)/6

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

Solve for x:

6^{x-1 }= 36^{x+2}

x = -5

What is the inverse of y = 4^{x}

f^{-1}(x) = log_{4}x

Write the explicit equation for the following sequence:

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

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

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

[-2,-1]

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}

Solve for x:

4*3^{x-1} = 14

x=2.14

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

No, inverse is y=log_{2}x

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

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

Write an equation for the amount of material left in the form A(t) = A_{o}e^{-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}

Solve for t:

300 = 200e^{t/4}

t=1.62

is the point is the point (2,25) a point on the inverse of the function f(x)=log_{5}x

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

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.

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