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Step-by-step explanation:

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The exponential growth function is

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 ....(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),

  .....(2)

....(3)

Divide equation (3) by (2),

The rate factor is b=1.8

Now, Substitute the value of a and b in equation (1)

Therefore, The exponential growth function is