N=NOe^-kt
N=mass at time t
NO = initial mass
k= 0.1476
t= time, in days
We are asked to find the half-life, which means you want to find how long it will take for half of the substance to decay/disappear (depending on situation).
If we are looking for half-life, we can simply set N to half of NO (which we are given a value of 40grams for)
Therefore:
N = 20
NO = 40
plugging these values and the value given for k back into the equation you get:
20 = 40e^-0.1476(t)
We are looking for t, so we have to manipulate the formula to get t by itself on one side of the equation.
We can start by dividing 40 from both sides, and you get:
0.5 = e^-0.1476(t)
We have the exponential function "e".
To get rid of e, we can use natural log (ln)
if e^y=x then ln (x) = y
look back at our equation we can set
0.5 = x
-0.1476(t) = y
Rewriting it in natural log form:
ln (0.5) = -0.1476(t)
Plug in ln (0.5) on a calculator to find its value and we get:
-0.693147 = -0.1476(t)
*Note: normally, getting a negative value would suggest that we did something wrong, because you cannot have a negative value as your t (you cannot have negative days), but because there is a negative on both sides of the equation, they will cancel out in this case.
The last step is to simply divide both sides by -0.1476
therefore:
T = 4.696119
But it asks you for the answer to the nearest tenth (one place after decimal pt) so
T (half life) = 4.7 days
Hope that helps :)
Answer:
11.0 or 11
Step-by-step explanation:
(2.75 x 10⁵ ) / (2.25 x 10² )
= (2.75 / 2.25) x 10⁵⁻²
= 1.2 x 10³ times .
(That's 1,200 times as many.)
