Answer:
If you have a quantity X of a substance, with a decay constant r, then the equation that tells you the amount of substance that you have, at a time t, is:
C(t) = X*e^(-r*t)
Now, we know that:
We have 2000g of substance A, and it has a decay constant of 0.03 (i assume that is in 1/year because the question asks in years)
And we have 3000 grams of substance B, with a decay constant of 0.05.
Then the equations for both of them will be:
Ca = 2000g*e^(-0.03*t)
Cb = 3000g*e^(-0.05*t)
Where t is in years.
We want to find the value of t such that Ca = Cb.
So we need to solve:
2000g*e^(-0.03*t) = 3000g*e^(-0.05*t)
e^(-0.03*t) = (3/2)e^(-0.05*t)
e^(-0.03*t)/e^(-0.05*t) = 3/2
e^(t*(0.05 - 0.03)) = 3/2
e^(t*0.02) = 3/2
Now we can apply Ln(x) to both sides, and get:
Ln(e^(t*0.02)) = Ln(3/2)
t*0.02 = Ln(3/2)
t = Ln(3/2)/0.02 = 20.3
Then after 20.3 years, both substances will have the same mass.
Let the number of minutes be = x.
Cost per minute = 11 cents = 0.11
Phone Bill = Monthly fee + 0.11* x
Substituting from the question
20.82 = 3 + 0.11x
3 + 0.11x = 20.82
0.11x = 20.82 - 3
0.11x = 17.82
x = 17.82/0.11
x = 162
<span>Lamar was billed for 162 minutes.</span>
Answer:
Step-by-step explanation:
when a rotation of 180 ° happens, it switches the (x,y) coordinates from (x,y) to (-x,-y) .. that's alll... soo for M then, of (3,4) it switches to M ' = ( -3, -4) see?
Answer:
That is has root -12 meaning if you replace x with -12 you get 0.
9514 1404 393
Answer:
A
Step-by-step explanation:
You can use x=0 and x=1 to find points that must be on the graph.
f(0) = 16·0.5^0 = 16
f(1) = 16·0.5^1 = 8
Only graph A matches these points.
