The decay of a substance can be modeled by the exponential decay formula:

A = P * e^(-kt)

where:
A is the amount of substance left after time t,
P is the initial amount of the substance,
k is the decay constant,
and t is the time.

In this case, we know that:
A = 1 gram (the amount of substance left),
P = 5 grams (the initial amount),
and k = 0.10 per hour (the decay rate).

We want to solve for t (the time it takes for the drug to decay to 1 gram). So we can plug in the known values and solve for t:

1 = 5 * e^(-0.10t)

First, divide both sides by 5:

1/5 = e^(-0.10t)

Then, take the natural logarithm of both sides to get rid of the exponential:

ln(1/5) = -0.10t

Finally, solve for t by dividing both sides by -0.10:

t = ln(1/5) / -0.10

Using a calculator, we find that:

t ≈ 16.1 hours

So, the closest answer is d.) 16.9 hours.

Question

The decay of a substance can be modeled by the exponential decay formula:

A = P * e^(-kt)

where:
A is the amount of substance left after time t,
P is the initial amount of the substance,
k is the decay constant,
and t is the time.

In this case, we know that:
A = 1 gram (the amount of substance left),
P = 5 grams (the initial amount),
and k = 0.10 per hour (the decay rate).

We want to solve for t (the time it takes for the drug to decay to 1 gram). So we can plug in the known values and solve for t:

1 = 5 * e^(-0.10t)

First, divide both sides by 5:

1/5 = e^(-0.10t)

Then, take the natural logarithm of both sides to get rid of the exponential:

ln(1/5) = -0.10t

Finally, solve for t by dividing both sides by -0.10:

t = ln(1/5) / -0.10

Using a calculator, we find that:

t ≈ 16.1 hours

So, the closest answer is d.) 16.9 hours.

Knowee AI · Accepted Answer