Derivatives of Exponential, Logarithmic & Trigonometric Functions

[alnadz]

Radioactive carbon isotopes have a half-life of 5715 years.
An object contains 1 gram of the isotopes. The amount A (in grams) that will be present after t years is
A = (1/2) . t/5715
At which rate is the amount changing when t = 10, 000 years?

 

[MarkFL]

Hello, and welcome to FMH!

I think you mean:

[MATH]A(t)=\left(\frac{1}{2}\right)^{\frac{t}{5715}}[/MATH]
What if we write:

[MATH]A(t)=e^{-\frac{\ln(2)}{5715}t}[/MATH]
Can you proceed?