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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?
\[ k = \_\_\_\_\_ \] (Round your answer to at least 5 decimal places)

2. How many bacteria are in the dish after 14 hours?
There are approximately \_\_\_\_\_ bacteria after 14 hours. (Round your answer to at least 5 decimal places)

Answer :

Answer:

Therefore, the answers are:

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

2.) There are approximately 676.29212 bacteria after 14 hours

Step-by-step 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.

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Rewritten by : Barada