the amount of radioactive substance prsent at anytime is given by q(t)=Q0e-0.1
How will it take for the radioactive substance x to decay to 30% of its original amount?
To find out how long it will take for the radioactive substance to decay to 30% of its original amount, we can set up an equation and solve for time (t).
Given the formula for the amount of radioactive substance at any time:
q(t) = Q₀e^(-0.1t)
We need to find the time when q(t) equals 30% of the original amount, which is 0.3Q₀.
So, we can set up the following equation:
0.3Q₀ = Q₀e^(-0.1t)
First, let's simplify the equation:
0.3 = e^(-0.1t)
To isolate the variable "t", we can take the natural logarithm (ln) of both sides of the equation:
ln(0.3) = ln(e^(-0.1t))
Using the property of logarithms (ln(e^x) = x), the equation becomes:
ln(0.3) = -0.1t
Now, let's solve for "t":
t = ln(0.3) / -0.1
Using a calculator, we can evaluate ln(0.3) and compute the value of "t" to find out how long it will take for the radioactive substance to decay to 30% of its original amount.