a radioactive substance decays 10% in 5 days. The amount remains after 20 days?

You need to determine k, the rate constant and I would do it this way.

ln(No/N) = kt
No = 10
N = 90
k = solve for this
t = 5 days.

Then knowing k, redo
ln(No/N) = kt
No = 100
N = Solve for this.
k from above
t = 20 days

How

To find the amount of a radioactive substance that remains after a specific amount of time, we can use the concept of exponential decay. The general formula for exponential decay is given by:

A = A₀ * (1 - r)^t

Where:
- A is the amount remaining after time t
- A₀ is the initial amount
- r is the decay rate (expressed as a decimal)
- t is the time elapsed

In this case, the substance decays by 10% (0.1) every 5 days. To calculate the amount remaining after 20 days, we can substitute the values into the formula:

A = A₀ * (1 - r)^t

A = 100 * (1 - 0.1)^(20/5)

A = 100 * (0.9)^4

A ≈ 65.61

Therefore, approximately 65.61% of the radioactive substance remains after 20 days.