Respuesta :
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
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