Answer:
An exponential growth function is given by:
[tex]f(x)=y=ab^x[/tex] .....[1]where a is the initial value and b is the growth factor.
As per the given statement: Fiona started her study of bacteria growth with 1,000 bacteria in a petri dish.
⇒Initial value(a) = 1000
Also, it is given that: After 1 hour, the count was increased to 1,800. After 2 hours, the count was 3,240. also, After the third hour showed a count of 5,832,
Let x represents the time in hour and y represents thee count of bacteria.
Then; from the statement we have;
[tex](1, 1800)[/tex] and (2, 3240)
Now, using these point we find the exponential growth function;
Substitute these in [1] we get;
[tex]1800 = ab[/tex] .....[2]
[tex]3240 =ab^2[/tex] ....[3]
Divide equation [3] by [2] we get;
[tex]\frac{3240}{1800}=\frac{ab^2}{ab}[/tex]
Simplify:
[tex]1.8 = b[/tex]
Now, substitute the value of a =1000 and b = 1.8 in [1] we get;
[tex]f(x) = 1000 \cdot (1.8)^x[/tex]
Therefore, the exponential growth function is, [tex]f(x) = 1000 \cdot (1.8)^x[/tex]
