Answer:
The exponential growth function is \(f(x) = 1000 \cdot (1.8)^x\)
Step-by-step explanation:
Given : Fiona started her study of bacteria growth with 1,000 bacteria in a Petri dish. After 1 hour, the count was increased to 1,800. After 2 hours, the count was 3,240. After the third hour showed a count of 5,832. Fiona wrote an equation to represent the exponential growth of the bacteria.
To find : What exponential growth function did Fiona write?
Solution :
The general form of an exponential function is \(y=ab^x\)....(1)
Where, a is the initial value and r is the rate factor.
According to question,
Initial value is a=1000
After 1 hour, the count was increased to 1,800.
After 2 hours, the count was 3,240.
After the third hour showed a count of 5,832,
Let x represents the time in hour and y represents thee count of bacteria.
Taking the points (1,1800), (2,3240).
Substitute in equation (1),
\(1800 = ab\) .....(2)
\(3240 =ab^2\) ....(3)
Divide equation (3) by (2),
\(\frac{3240}{1800}=\frac{ab^2}{ab}\)
\(1.8=b\)
The rate factor is b=1.8
Now, Substitute the value of a and b in equation (1)
\(f(x) = 1000 \cdot (1.8)^x\)
Therefore, The exponential growth function is \(f(x) = 1000 \cdot (1.8)^x\)
