Exponential/logarithmic functions –word problems

You can model exponential growth or decay with:

tray )1(

rtPeA

tn

n

rPA )1(

Used with Growth or decay.

Money with interest compounded annually

Used for Money with interest compounded “n”

number of times

Used for Money with interest compounded

continuously.

31.8x

Example with MONEYIf you invest $2000 in a savings account that

pays 5% annual interest. How much money will you have after six years?

How many years will it take for the account to grow to at least $3000?

tray )1( 6)05.1(2000 y 19.2680$

x)05.1(20003000

It will take exactly 8.31 years

Formula? Plug into formula answer

formula

answerx)05.1(5.1 x5.1log 05.1

Isolate the base Log form

More MoneySuppose you deposit $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account after 4 years?

rtpea 405.03000 ea 21.3664$Formula? Plug into formula answer

How long will it take for your money to triple? Assuming you don’t withdraw or deposit any more money?

97.21x

xe 05.030009000formula

answerxe 05.03 x05.03ln Isolate the base Log form

It will take exactly 21.97 years for you money to triple. (21 years 11 months and 20 days)

Money, Money, MoneySuppose you deposit money into an account

paying 7.4% interest compounded quarterly (4 times a year) how long will it take for you money to double?

45.9x

tn

n

rpa )1(formula

answerx40185.12 x42log 0185.1 Isolate the base Log form

tpa 4)4

074.1(Plug in what we know t 4)

4

074.1(2What’s the starting

or ending amount?

It will take exactly 9.45 years for you money to double. (9 years 5 months and 13 days)

Real-lifeA spacecraft can only attain a stable orbit 300 km

above the earth if it reaches a velocity of 7.7 km/s. Suppose a rocket has a mass ratio (R) of 25, a firing time (t) of 100 s and an exhaust velocity (c) of 2.8 km/s. Use the formula below to find if the spacecraft attain a stable orbit 300 km above the earth’s surface? Rctv ln0098.0

)25ln()8.2()100(0098.0 v033.8v

ExampleA new car is worth $20,000 and is expected

to depreciate 12% each year. How much will the car be worth after 10 years?

How long will it take for the car to be worth half it’s original value?

PracticePg 439 #26, 27, 28, 31, 32