Question

Suppose there are 40 bacteria in a Petri dish at a certain time. Ten hours later, there are 220 bacteria in

the dish.
1.) What is the growth constant, k, for this problem?
2.) How many bacteria are in the dish after 14 hours?
Round your answer to at least 5 decimal places.
bacteria after 14 hours.
1.) k =______ round your answer to at least 5 decimal places
2.) There are approximately ______ bacteria after 14 hours

Answer 1

Therefore, the answers are:

1.) k = 0.15504 (rounded to 5 decimal places)

2.) There are approximately 676.29212 bacteria after 14 hours

Explanation:

To find the growth constant, k, we can use the exponential growth formula:

N(t) = N₀ * e^(kt)

where N(t) is the number of bacteria at time t, N₀ is the initial number of bacteria, e is the base of the natural logarithm (approximately 2.71828), and k is the growth constant.

Given that there are 40 bacteria initially (N₀ = 40) and 220 bacteria after 10 hours (N(10) = 220), we can set up the following equation:

220 = 40 * e^(k * 10)

To solve for k, we can divide both sides of the equation by 40 and take the natural logarithm of both sides:

ln(220/40) = ln(e^(k * 10))

Simplifying further:

ln(5.5) = (k * 10)

Dividing both sides by 10:

k = ln(5.5) / 10

Using a calculator, we can find that k is approximately 0.15504 (rounded to 5 decimal places).

Now, to find the number of bacteria after 14 hours, we can use the exponential growth formula again:

N(14) = N₀ * e^(k * 14)

Substituting N₀ = 40 and k = 0.15504:

N(14) = 40 * e^(0.15504 * 14)

Calculating this expression, we find that N(14) is approximately 676.29212 (rounded to 5 decimal places).

I hope you helped.