a population doubles in size every 15 years. assuming exponential growth, find the (a) annual growth rate (b) continuous growth rate

Sagot :

The annual growth rate is 4.73 %

The continuous growth rate is 4.62 %

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

Let us assume:

The initial amount of 1, so results are 2.

Let x be the  percent in decimal form

Growth rate per year:

[tex]1(1+x)^{15} = 2[/tex]

Take ln on both the sides

[tex]ln((1+x)^{15}) = ln(2)[/tex]

15*ln(1+x) =0 .693

ln(x+1) = 0.693/15

ln(x+1) = 0.04621

Take anti ln on both the sides

x+1 = 1.0473

x = 1.0473 - 1

x = .0473

x =4.73 % annual growth rate

Continuous growth rate:

[tex]1*e^{15x} = 2[/tex]

[tex]ln(e^{15x}) = ln(2)[/tex]

15x*ln(e) = ln(2)

ln(e) = 1

15x =0.693

x =0 .693/15

x = .0462

x = 4.62 %

To learn more about the exponential growth function from the given link

https://brainly.com/question/13223520

#SPJ4