Exponential/logarithmic functions –word problems.

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Presentation transcript:

Exponential/logarithmic functions –word problems

You can model exponential growth or decay with: 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.

Example with MONEY If 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? It will take exactly 8.31 years Formula? Plug into formulaanswer formula answer Isolate the base Log form

More Money Suppose you deposit $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account after 4 years? 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? formula answer Isolate the base Log form It will take exactly years for you money to triple. (21 years 11 months and 20 days)

Money, Money, Money Suppose 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? formula answer Isolate the base Log form Plug in what we know What’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-life A 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?

Example A 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?

Practice Pg 439 #26, 27, 28, 31, 32