Answer:
Step-by-step explanation:
Answer:
I think that the answer is C
Answer:
Step 3
Step-by-step explanation:
The solution is given in the image attached. The steps are:
Step 1:
Step 2: simplifying the coefficients of x:
Step 3: Adding 1/4 to both sides
Step 4: Multiplying both sides by 5/7
The addition property of equality states that if a number is added to both sides of an equation, the equation is still valid (i.e the equation is still the same). From the steps above, The addition property of equality was applied in step 3
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 :)
