Question

A mass of 100 grams of a particular radioactive substance decays according to the function m(t)=100e−t850

Answer 1

Answer:

After 1023.4 years the mass of the substance will be 30 g.

Explanation:

Hi there!

Let´s write the function (according to what I found on the web):

$m(t) = 100e^{-t/850}$

We have to find the time "t1" at which the mass of the substance is 30 g. Mathematically:

m(t1) = 30

Then:

$30 = 100e^{-t1/850}$

Let´s solve the equation for t1. First, divide by 100 both sides of the equation:

$0.3 = e^{-t1/850}$[/tex]

Apply ln to both sides of the equation:

$ln(0.3) = ln(e^{-t/850})$

Use the logarithm property: ln (aᵇ) = b ln(a)

ln(0.3) = -t/850 · ln (e)             (ln (e) = 1)

ln(0.3) = -t/850

850 ln(0.3) = -t

t = -850 ln(0.3)

t = 1023.4

After 1023.4 years the mass of the substance will be 30 g.