Answer:
The initial mass of the sample was 16 mg.
The mass after 5 weeks will be about 0.0372 mg.
Step-by-step explanation:
We can write an exponential function to model the situation.
Let the initial amount be A. The standard exponential function is given by:
Where r is the rate of growth/decay.
Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:
After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.
Therefore, when x = 12, P(x) = 2. By substitution:
Solve for A. Simplify:
Simplify:
Thus, the initial mass of the sample was:
5 weeks is equivalent to 35 days. Therefore, we can find P(35):
About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.
1. Slope intercept form. First find two points to get slope: (0,-3) and (-3,-4). Slope is
(-4 - -3)/(-3 - 0)= 1/3
Use one of the points of (x,y) to solve for b
Y=1/3x + b
-3 = 1/3(0) + b
-3 = b so your slope intercept equation is
Y = 1/3x - 3
2. Rate of Change is slope. Your points are (0,10) and (24,6) so slope is (6-10)/(24-0)
= - 1/6 which means that for each 1 unit increase in x, y decreases by 1/6.
3. Standard form is ax + by =c
Notice it is the same line as in the first graph so it's the same equation
y = 1/3x - 3
First, you cannot have fractions, so you have to multiply the equation by 3 to get rid of the 1/3.
3y= x - 9. Now move the x over:
-x + 3y = - 9. Now get rid of the negative value on x by multiplying the entire equation by -1:
x - 3y = 9
Answer:
First Question = 16 Second Question = 8
Step-by-step explanation:
First one
32+48=x(2+3)
80=5x
Divide each sides with 5 and you have x=16
Second one
32+48=4(x+12)
80=4x+48
subtract 48 from 48 and 80 and you have 32=4x.
Divide it with 4 both side and you have x=8
Answer:
c
Step-by-step explanation:
sepse nuk me intereson se ca thua ti jevg dreqi i cmen
Times 2nd equation by 2
add to first equation
3x+6y=6
<u>4x-6y=8 +</u>
7x+0y=14
7x=14
divide both sides by 7
x=2
sub back
2x-3y=4
2(2)-3y=4
4-3y=4
minus 4 both sideds
-3y=0
y=0
(x,y)
(2,0)
