Applications of Exponents

1 / 16

# Applications of Exponents - PowerPoint PPT Presentation

Applications of Exponents. Solve real life applications using exponents. Simple Interest. If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r, expressed as a decimal, the interest I charged is I = Prt. Payment period. Annually once a year

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Applications of Exponents' - roz

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Applications of Exponents

Solve real life applications using exponents

Simple Interest

If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r, expressed as a decimal, the interest I charged is

I = Prt

Payment period

Annually once a year

Semiannually twice a year

Quarterly four times a year

Monthly 12 times a year

Daily 365 times a year

Compounded Interest

When the interest is due at the end of a payment period is added to the principle so that the interest computed at the end of the next payment period is based on this new principle amount (old principle + interest), the interest is said to be compounded. Compound interest is interest paid on principle and previously earned interest

Compound interest formula

A = accumulated value or future value

t = time P = principle r= annual interest rate

n = compounded that many times

A = P(1+ )nt

Example

Investing \$1000 at an annual rate of 10% compounded annually, semiannually, quarterly monthly and daily will yield what amounts after 1 year?

Continuous Compounding

The amount A after t years due to a principle P invested at an annual interest rate r compounded continuously

A = Pert

The amount A that results from investing a principle P of \$1000 at an annual rate r of 10% compounded continuously for a time t of 1 year is?

Effective rate of interest

The effective rate of interest is the equivalent annual simple rate of interest that would yield the same amount as compounding after 1 year.

Computing the value of an IRA

IRA (individual retirement account)

On January 2, 2004 I put \$2000 in an IRA that will pay interest 10% per annum compounded continuously.

• What will the IRA be worth when I retire in 2035?
• What is the effective rate of interest?
Present Value Formulas

The present value P of A dollars to be received after t years, assuming a per annum interest rate r compounded n times per year is

P = A( 1+ )-nt

If the interest is compounded continuously then

P = Ae-rt

Doubling and Tripling Time for an investment

How long will it take for an investment to double in value if it earns 5% compounded continuously?

How long will it take to triple at this rate?

Exponential Growth and Decay

Many natural phenomena have been found to follow the law that an amount A varies with time t according to

A(t) = A0ekt

where A0= A(0) is the original amount (t=0) and k≠0 is a constant.

If k>0 then the above equation is said to follow the exponential law or the law of uninhibited growth.

If k<0 is said to follow the law of uninhibited decay

Uninhibited growth of cells

A model that gives the number N of cells in the culture after a time t has passed (in the early stages of growth is)

N(t) = N0ekt, k>0

Where N0 = N(0) is the initial number of cells and k is a positive constant that represents the growth rate of the cells

The amount A of a radioactive material present at time t is given by

A(t) = A0ekt k<0

Where A0 is the original amount of radioactive material and k is negative number that represents the rate of decay.

Half life

All radioactive substances have a specific half life which is the time required for half of the radioactive substance to decay.

Newton’s Law of Cooling

Newton’s Law of Cooling states that the temperature of a heated object decreases exponentially over time toward the temperature of the surrounding medium

The temperature u of a heated object at a given time t can be modeled by the following function

u(t) = T +(u0-T)ektk<0

Where T is the constant temperature of the surrounding medium, u0 is the initial temperature of the heated object, and k is a negative constant.