Growth and Decay

Warm-up

More logs quiz and HW/INB check!

Learning Objective: to use logarithms to solve real life situations.

NotesGeneral Formula for Growth and Decay:

kty ne y = final amount

n = initial amount

k = a constant (for growth k > 0, decay k < 0

t = time

Ex 1 - A certain culture of bacteria will grow from 500 to 4000 bacteria in 1.5 hours. Find the constant, k, for the growth formula. kty ne

4000 500ek 1.5

8 1.5keln8 1.5ln keln8 1.5k

1.3863k

The time it takes for half a sample to decompose is called its half-life.

Ex 2 - If the half-life of a 200-gram sample of an element is 10 years, find the constant, k.

kty ne100 200e

k 10

.5 10keln .5 10ln keln .5 10k

.0693k

Ex 3 - A piece of machinery valued at $25,000 depreciates at a steady rate of 10% yearly. When will the value be $5,000? Use the formula:

1n

nV P r

5000 25000 1 .1n

.2 .9 n

log.9 .2 nlog.2

log.915.3 years

HW – Applications of logs wksht

Summary – Logarithms are useful because…

Out – none

Don’t forget about POW!!