Hard math problems. Please help.

Carbon Dating. The amount of carbon-14 present in animal bones after t years is given by Pₒe^0.00012t. A bone has lost 31% of its carbon-14. How old is the bone?

The sales S of a product have declined in recent years. There were 201 million sold in 1984 and 1.4 million sold in 1994. Assume the sales are decreasing according to the exponential decay model, S(t)=Sₒe^-kt
A) Find the value k and write an exponential function that describes the number sold after time t in years since 1984.
B)Estimate the sales of the product in the year 2002.
C)In what year (theoretically) will only 1 of the product be sold?

Thanks for all of your help.

Hi ?, first of all there is no "hard" maths, it is only difficult maths.
Ok. now the given expression has to be P = Po e^ - 0.00012 t
Negative sign is missing.
Ok. 31% lost. So it means 69% remains. Hence P/Po = 0.69
Therefore 0.69 = e^ - 0.00012 t
Rearranging, t = (1/0.00012)* ln (1/0.69) = 3092 years

Let us take So = 201 million and S = 1.4 million. t = 10 years.
Hence e^10 k = 201/1.4
or k = ln ( 201/1.4) / 10 = 0.497
So required k = 0.497.
a) Hence S = So e^ - 0.497 t
b) Now required S when t = 18 years is got right from S1 = So e^ - 0.497(18)
Hope knowing So as 201 million, you can solve for S1.
c) now 1 = 201 e^ - 0.497 t
So t can be solved as before. Hope you would that using natural logarithm