What is the thickness of the hull walls will ensure that less than 1% of the radiation will pass through? By using the formula p= 100(0.2)^x
To find the thickness of the hull walls that will ensure less than 1% of radiation passing through, we need to solve the equation p = 100(0.2)^x, where p represents the percentage of radiation passing through and x represents the thickness of the hull walls.
We want to find the value of x that results in p less than 1%. Let's rewrite the equation as:
0.2^x = 1/100
To solve for x, we take the logarithm of both sides using base 0.2 (since 0.2 is the value raised to the power of x):
log base 0.2 (0.2^x) = log base 0.2 (1/100)
x = log base 0.2 (1/100)
Using the change of base formula, we can convert the logarithm to base 10:
x = log base 10 (1/100) / log base 10 (0.2)
Using a calculator:
x ≈ 3.322 / (-0.69897)
x ≈ -4.74836
The negative value of x does not make sense in this context, as thickness cannot be negative. Therefore, there is no positive value of x that will ensure less than 1% of radiation passing through.