Question

suppose a substance decays at a yearly rate equal to half the square of the mass of the substance present. if we start with 50 g of the substance, how long will it be until only 25 g remain?

Answer 1

The substance will take approximately 1.386 years to decay from 50 g to 25 g.

Step-by-step explanation:

The substance in question undergoes decay at a rate equal to half the square of its mass. Starting with 50 g of the substance, we need to find out how long it will take for only 25 g to remain.

Let's assume that after t years, only half (25 g) of the original mass remains. We can use the formula for exponential decay to solve for t:

25 = 50 * e^(-0.5t)

Dividing both sides by 50, we get:

0.5 = e^(-0.5t)

Taking the natural logarithm of both sides:

ln(0.5) = -0.5t

Solving for t, we find:

t = (ln(0.5)) / -0.5

Using a calculator, we can evaluate this expression and find that it will take approximately 1.386 years for only 25 g of the substance to remain.