Example of Exponential Growth, Study notes of Mathematics

Example of exponential growth problems

Typology: Study notes

2019/2020

Uploaded on 10/12/2020

caitlyn-dojillo-masgong
caitlyn-dojillo-masgong 🇵🇭

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2 months ago you had 3 mice, you now have 18. Assuming the growth continues
like that.
What is the "r" value?
Given:
A=18
P=3
t=2 months
r=?
Formula: A=Pert
Substitute the values:
18 = 3e2r (Multiplication operation has a COMMUTATIVE PROPERTY, 2*r = r*2)
Divide both sides by 3: 6 = e2r
Take the natural logarithm of both sides: ln(6) = ln(e2r)
ln(ex)=x,
so: ln(6) = 2r
Swap sides: 2r = ln(6)
Divide by 2: r = ln(6)/2
r=0.896

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2 months ago you had 3 mice, you now have 18. Assuming the growth continues like that. What is the "r" value? Given: A= P= t=2 months r=? Formula: A=Pert Substitute the values: 18 = 3e2r^ (Multiplication operation has a COMMUTATIVE PROPERTY, 2r = r2)

Divide both sides by 3: 6 = e

2r

Take the natural logarithm of both sides: ln(6) = ln(e2r)

ln(ex)=x ,

so: ln(6) = 2r

Swap sides: 2r = ln(6)

Divide by 2: r = ln(6)/

r=0.