Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

Step-by-step explanation:

The amount of Carbon-14 after t years is given by the following equation:

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.

This means that

How many years will it take for carbon–14 to decay to 10 percent of its original amount?

This is t for which:

So

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47