Alex gets injections of a medicinal drug - Leaving Cert Mathematics - Question 9 - 2022

To find the time when there is exactly 1 mg of the drug left, we set up the equation:

$$15(0.6)^t = 1$$

Dividing both sides by 15:

$$(0.6)^t = \frac{1}{15}$$

Taking the logarithm of both sides:

$$\log(0.6)^t = \log\left(\frac{1}{15}\right)$$

Using the property of logarithms, we have:

$$t \cdot \log(0.6) = \log(1) - \log(15)$$

We can solve for t:

$$t = \frac{\log(1) - \log(15)}{\log(0.6)}$$

This simplifies to:

$$t \approx 5.3 \text{ days}$$

Thus, it will take approximately 5.3 days for there to be exactly 1 mg of the drug left.