Answer:
An exponential growth function is given by:
\(f(x)=y=ab^x\) .....[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;
\((1, 1800)\) and (2, 3240)
Now, using these point we find the exponential growth function;
Substitute these in [1] we get;
\(1800 = ab\) .....[2]
\(3240 =ab^2\) ....[3]
Divide equation [3] by [2] we get;
\(\frac{3240}{1800}=\frac{ab^2}{ab}\)
Simplify:
\(1.8 = b\)
Now, substitute the value of a =1000 and b = 1.8 in [1] we get;
\(f(x) = 1000 \cdot (1.8)^x\)
Therefore, the exponential growth function is, \(f(x) = 1000 \cdot (1.8)^x\)
