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

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 $f(x) = 1000 \cdot (1.8)^x$