Mat 117 Fall 2011 Instructor: Dr. Firoz November 1, 2011

MAT 117

  1. Composition of functions:

a)Given . Find

b)Given . Find

c)Use the given table to find

x / / / / /
/ 2 / 2 / 1 / 0 / 3
/ 0 / -1 / 2 / 1 / 5

d)Find the domain of where

e)Find the domain of where

  1. Finding inverse of a one-to-one function:

a)

b)

c)

  1. Solve the exponential functions:

a)

b)

c)

d)

e)

  1. Solve for the logarithmic functions:

a)

b)

c)

d)

  1. Write the corresponding logarithmic form:

a)

b)

c)

  1. Write the corresponding exponential form.

a)

b)

c)

  1. Use logarithmic properties to simplify:

a)

b)

c)

  1. Write as a sum and/or difference:

a).

b)

  1. Write as a single logarithmic form:

a)

b)

c)

d)

  1. Find the domain:

a)

b)

c)

  1. The total amount of an investment of $p for t years at a compound interest rate r% for n times a year is modeled by . Use the formula to calculate the following:

a)Find the total amount if $500 is invested at 10% interest compounded yearly for 2 years.

b)Find the total amount if $500 is invested at 10% interest compounded semiannually for 2 years.

c)Find the total amount if $500 is invested at 10% interest compounded weekly for 2 years.

d)Find the total amount if $500 is invested at 10% interest compounded monthly for 2 years.

e)Find the total amount if $500 is invested at 10% interest compounded biweekly for 2 years.

f)Find the total amount if $500 is invested at 10% interest compounded daily for 2 years.

g)How long will it take a sum of money to double at 5% interest compounded quarterly?

  1. The total amount of an investment of $p for t years at a continuous compounding interest rate r% modeled by. Use the formula to calculate the following:

a)How much to invest now to get $2000 in 5 years at a rate of 6% compounded continuously?

b)Find the total amount in the fund if $6000 is invested at 4% interest compounded continuously for 2 years.

  1. (Growth model) The size P of a certain insect population at time t (in days) is modeled by . Find the following:

a)The initial size of the population

b)The growth rate

c)The population for t = 10

d)When will the population reach 160?

e)When will the population double

  1. (Decay model) The size P of a certain insect population at time t (in years) is modeled by , where is the initial population for t = 0. Find the following when the initial population is known as 500 insects:

a)The decay rate (include negative sign in your answer)

b)How many insects is left after 20 years (round to nearest integer)

c)When will 400 insects be left (round to nearest tenth)?

d)What is the half life (round to nearest tenth)?

  1. The half life of radium is 1690 years. If 80 grams of radium are present now, how much will be in 450 years (round to three decimal places?

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Class activity: 11/01/2011Your name:

  1. The half life of radium is 2000 years. If 100 grams of radium are present now, how much will be in 500 years (round to three decimal places?
  1. (Decay model) The size P of a certain insect population at time t (in years) is modeled by , where is the initial population for t = 0. Find the following when the initial population is known as 400 insects:

e)The decay rate (include negative sign in your answer)

f)How many insects is left after 20 years (round to nearest integer)

g)When will 600 insects be left (round to nearest tenth)?

h)What is the half life (round to nearest tenth)?

  1. Find the total amount if $500 is invested at 10% interest compounded quarterly for 5 years.

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