As pure 1 mathematics

The rate of decay of a radioactive substance is proportional to the number, N, of radioactive atoms present at time t
a )Write an equation representing this information
b )Sketch a graph of N against t
c )What is the sign of d^2n/dt^2
Please help to solve this question.

"The rate of decay of a radioactive substance is proportional to the number, N, of radioactive atoms present at time t"

Can you translate this sentence into mathematics?

I think it will be like deceleration
dn/dt=-kn

I’m not sure what exactly you’re referring to when you compare this to deceleration, but the eqn you have is good.

You can even solve this ODE if you can’t sketch it from the ODE eqn.

This is my graph. Is it correct?