Question

Carbon-14 is an element that loses about 10% of its mass every millennium (ie., 1000 years). A sample ofCarbon-14 has 600 grams.Which graph shows the sample's mass y (in grams) after 3 millennia?(i will send the answer choices)

Answer 1

Given that:

Rate at which Carbon-14 loses its mass = 10%

Initial mass of the sample of Carbon-14 = 600 g

The formula for the decreasing growth rate is of the form

$y(t)=a(1-r)^t$

where

y = S(t) = mass of the sample after t millennia

x = t = number of millennia

a = Initial mass = 600 grams

r = decay rate = 10% = 0.1

Plug the values into the formula.

$\begin{gathered} S(t)=600(1-0.1)^t \\ =600(0.9)^t \end{gathered}$

The function that gives the sample's mass after t millennia, S(t), in t millennia from today is

$S(t)=600(0.9)^t$

Graph the function S(t).

Option A is correct.