Answer:
f(x)= 10,000(2)^x
Step-by-step explanation:
Exponential equations can be modeled by a(r)^x where a is the initial amount, r is the difference, and x is how many units the equation should be squared by.
A function that describes the bacteria population after d days would be,[tex]\bold{f(d) = 10000\times(1+0.15)^d}[/tex]
An exponential growth function is a function that grows at a constant percent growth rate.
f(t) = a×(1 + r)^(t)
where f(t) = exponential growth function
a = initial amount
r = growth rate
t = number of time intervals
For given example,
initially a bacteria population (a) = 10,000
Five days later, they find that the population has doubled.
d = 5, f(5) = 20,000
Assuming it grows exponentially, we find the growth rate of a bacteria population by using the formula of exponential growth function.
[tex]\Rightarrow f(d) = a\times(1 + r)^{d}\\\\\Rightarrow f(5) = 10000\times (1+r)^5\\\\\Rightarrow 20000=10000\times (1+r)^5\\\\\Rightarrow 2=(1+5)^5\\\\\Rightarrow 1+r=\sqrt[5]{2}\\\\\Rightarrow 1+r = 1.15\\\\\Rightarrow r = 1.15-1\\\\\Rightarrow \bold{r = 0.15}\\\\\Rightarrow \bold{r=15\%}[/tex]
This means, the exponential growth function would be,
[tex]\bold{f(d) = 10000\times(1+0.15)^d}[/tex], where d represents number of days.
Learn more about exponential growth here:
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