Question

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. What exponential growth function did Fiona write?

Answer 1

F (x)=1000×1.8^x is the equation.

Answer 2

The exponential growth function is
`f(x) = 1000 \cdot (1.8)^x`

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),

`(3240)/(1800)=(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`