Find C for P(t) = Ce-Ct Given 70% Probability of Surviving 2+ Years

[apiwowar]

p(t) = Ce^-Ct

i know P(t) is the fraction of the group surviving t years or less

now the question is: suppose a patient has a 70% probability of surviving at least 2 years, find C.

to find c i would take the integral of p(t) but what would my limits be? surviving 2 at least 2 years, so that's more than 2 years. would i have my lower limit be 2 and then have my upper limit be infiniti or just a big number?

any help would be appreciated

 

[Tinyboss]

Not my field, but compute $$\int_0^xCe^{-Ct}dt$$. What's the limit as x goes to infinity? Does it depend on C?

I think you want to find C so that the integral from 0 to 2 years equals 70% of the integral from 0 to infinity.