About 10% of lung cancer patients are cured of the disease, i.e., they survive 5 years after diagnosis with no evidence that the cancer has returned. Only 14% of lung cancer patients survive 5 years after diagnosis. Assume that the fraction of incurable lung cancer patients that survives a time t after diagnosis is given by S(t) = e^(-kt).

Question

About 10% of lung cancer patients are cured of the disease, i.e., they survive 5 years after diagnosis with no evidence that the cancer has returned. Only 14% of lung cancer patients survive 5 years after diagnosis. Assume that the fraction of incurable lung cancer patients that survives a time t after diagnosis is given by S(t) = e^(-kt).

Find an expression for the fraction S(t) of lung cancer patients that survive a time "t" after being diagnosed with the disease. Be sure to determine the values of all of the constants in your answer.
What fraction of lung cancer patients survives two years with the disease?

Answer 1

I believe 10% are cured, 14% survived so only 4 % or 1/25 are incurable that survive?

Answer 2

STILL UNSOLVED

Answer 3

To find the expression for the fraction S(t) of lung cancer patients that survive a time "t" after being diagnosed with the disease, we are given the information that S(t) = e^(-kt), where t is the time in years.

We are also given that 10% of lung cancer patients are cured of the disease, meaning they survive 5 years after diagnosis with no evidence of cancer returning. This implies that S(5) = 0.10.

Using the given information, we can substitute t = 5 and S(5) = 0.10 into the equation to solve for the constant k:

0.10 = e^(-5k)

To solve for k, we need to take the natural logarithm (ln) of both sides of the equation:

ln(0.10) = ln(e^(-5k))

Using the property of logarithms (ln(a^b) = b * ln(a)):

ln(0.10) = -5k * ln(e)

Since ln(e) is equal to 1:

ln(0.10) = -5k

Now, we can solve for k by dividing both sides of the equation by -5:

k = ln(0.10) / -5

Using a calculator, we can find the value of k:

k ≈ -0.22314355

So, the expression for the fraction S(t) of lung cancer patients that survive a time "t" after being diagnosed is:

S(t) = e^(-0.22314355t)

Now, we can calculate the fraction of lung cancer patients that survive two years with the disease by substituting t = 2 into the expression:

S(2) = e^(-0.22314355 * 2)

Using a calculator, we can find the value of S(2):

S(2) ≈ 0.54881164

Therefore, approximately 54.88% of lung cancer patients survive two years with the disease.