Scientists are studying the growth of a strain of bacteria - Scottish Highers Maths - Question 6 - 2016

To find the time taken for the number of bacteria to double, we set the equation for doubling:

$B(t) = 2 \times B(0) = 2 \times 200 = 400.$

Using the original formula:

$400 = 200e^{0.1t}.$

Dividing both sides by 200 gives:

$2 = e^{0.1t}.$

Taking the natural logarithm of both sides:

$\ln(2) = 0.1t.$

Now, solve for $t$:

$t = \frac{\ln(2)}{0.1}.$

Using a calculator:

$t \approx \frac{0.693}{0.1} \approx 6.93 \text{ hours.}$

Therefore, the time taken for the number of bacteria to double is approximately 6.93 hours.