The area, A mm², of a bacterial culture growing in milk, t hours after midday, is given by A = 20e^{0.15t}, t ≥ 0 (a) Write down the area of the culture at midday. (b) Find the time at which the area of the culture is twice its area at midday. Give your answer to the nearest minute.

A-Level Edexcel Maths Pure Trigonometric Functions: The area, A mm², of a bacterial

The area, A mm², of a bacterial culture growing in milk, t hours after midday, is given by A = 20e^{0.15t}, t ≥ 0 (a) Write down the area of the culture at midday - Edexcel - A-Level Maths Pure - Question 6 - 2012 - Paper 6

Question 6

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The area, A mm², of a bacterial culture growing in milk, t hours after midday, is given by A = 20e^{0.15t}, t ≥ 0 (a) Write down the area of the culture at midday. ... show full transcript

Worked Solution & Example Answer:The area, A mm², of a bacterial culture growing in milk, t hours after midday, is given by A = 20e^{0.15t}, t ≥ 0 (a) Write down the area of the culture at midday - Edexcel - A-Level Maths Pure - Question 6 - 2012 - Paper 6

Step 1

Write down the area of the culture at midday.

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Answer

To find the area at midday, we substitute $t = 0$ into the given formula:

$A = 20e^{0.15(0)} = 20e^{0} = 20 \text{ mm}^2.$

Thus, the area of the culture at midday is 20 mm².

Step 2

Find the time at which the area of the culture is twice its area at midday.

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Answer

We need to find the time when the area $A$ is twice the area at midday.

Thus, we set up the equation:

$A = 2 \times 20 = 40 \text{ mm}^2.$

Substituting into the area formula gives:

$40 = 20e^{0.15t}.$

Dividing both sides by 20:

$2 = e^{0.15t}.$

Taking the natural logarithm (ln) of both sides:

$\ln(2) = 0.15t.$

Now we solve for $t$ :

$t = \frac{\ln(2)}{0.15}.$

Calculating this:

$t \approx \frac{0.693147}{0.15} \approx 4.621.$

Converting to minutes:

$t \approx 4.621 \times 60 \approx 277.27 ext{ minutes}.$

Rounding to the nearest minute, we get:

277 minutes, or 4 hours and 37 minutes after midday.

The area, A mm², of a bacterial culture growing in milk, t hours after midday, is given by A = 20e^{0.15t}, t ≥ 0 (a) Write down the area of the culture at midday - Edexcel - A-Level Maths Pure - Question 6 - 2012 - Paper 6

Worked Solution & Example Answer:The area, A mm², of a bacterial culture growing in milk, t hours after midday, is given by A = 20e^{0.15t}, t ≥ 0 (a) Write down the area of the culture at midday - Edexcel - A-Level Maths Pure - Question 6 - 2012 - Paper 6

Write down the area of the culture at midday.

Find the time at which the area of the culture is twice its area at midday.

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