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Sagot :
The initial population of 100 that doubles in 9 years, gives the
expression for population as; [tex]\underline{ P = 100 \cdot e^{0.077 \cdot t}}[/tex].
How can the expression for the population be found?
Given parameters are;
The time it takes the population to double = 9 years
The initial population count = 100
Required:
The expression that gives the population after t years.
Solution:
The population as a function of time can be expressed as an
exponential function as follows;
[tex]P = \mathbf{P_0 \cdot e^{c \cdot t}}[/tex]
At the start, t = 0, P = 100, we have;
[tex]100 = \mathbf{ P_0 \times e^{c \times 0} }= P_0[/tex]
Therefore;
P₀ = 100
After 9 years, we have;
P = 2·P₀
Therefore;
[tex]2 = \mathbf{ e^{c \times 9}}[/tex]
ln(2) = 9·c
[tex]c = \dfrac{ln(2)}{9} \approx 0.077[/tex]
The function that gives the population is therefore;
- [tex]\underline{ P = 100 \cdot e^{0.077 \cdot t}}[/tex]
Learn more about exponential functions here:
https://brainly.com/question/15602335
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