Question

In a lab experiment, 40 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 17 hours. How many bacteria would there be after 4 hours, to the nearest whole number?

Answer 1

Using the exponential growth formula, we can calculate that the 40 bacteria will grow to approximately 44 bacteria after 4 hours, given the doubling period of 17 hours.

Step-by-step explanation:

To calculate how many bacteria there would be after 4 hours given that they double every 17 hours, we need to use the formula for exponential growth, which is N = N0 * 2(t/T), where N is the final amount, N0 is the initial amount, t is the time elapsed, and T is the doubling time.

Starting with 40 bacteria (N0 = 40), doubling every 17 hours (T = 17), and wanting to find the amount after 4 hours (t = 4), our equation will look like this:

N = 40 * 2(4/17)

Using a calculator, we find that 2(4/17) is approximately 1.099, which when multiplied by 40 gives us:

N ≈ 40 * 1.099 = 43.96

To the nearest whole number, there would be 44 bacteria after 4 hours.

Answer 2

59 bacteria would there be after 4 hours.

Step-by-step explanation:

Given:

Bacteria in the petri dish = 40

Time taken for the bacteria to be doubled =17 hours

To Find:

To Find the number bacteria left after 4 hours = ?

Solution:

By using the proportionality,

After 17 hours the number of bacteria will be 80.

Let the number of bacteria after 4 hours be x

then

`(80)/(17) = (x)/(4)`

Now by cross multiplication

`17 * x = 80 * 4`

`17 x = 320`

`x=(320)/(17)`

x= 18. 82

So the number of bacteria after 4 hours will be

= 40 + 18.82

= 58.82

=59