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?

f(x) = ( )x

Answer 1

I just finished doing this

Answer 2

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;

`(3240)/(1800)=(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`