Answer:
Given that,
The number of grams A of a certain radioactive substance present at time, in years
from the present, t is given by the formula
![A=45e^{-0.0045(t)}](https://tex.z-dn.net/?f=A%3D45e%5E%7B-0.0045%28t%29%7D)
a) To find the initial amount of this substance
At t=0, we get
![A=45e^{-0.0045(0)}](https://tex.z-dn.net/?f=A%3D45e%5E%7B-0.0045%280%29%7D)
![A=45e^0](https://tex.z-dn.net/?f=A%3D45e%5E0)
We know that e^0=1 ( anything to the power zero is 1)
we get,
![A=45](https://tex.z-dn.net/?f=A%3D45)
The initial amount of the substance is 45 grams
b)To find thehalf-life of this substance
To find t when the substance becames half the amount.
A=45/2
Substitute this we get,
![\frac{45}{2}=45e^{-0.0045(t)}](https://tex.z-dn.net/?f=%5Cfrac%7B45%7D%7B2%7D%3D45e%5E%7B-0.0045%28t%29%7D)
![\frac{1}{2}=e^{-0.0045(t)}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3De%5E%7B-0.0045%28t%29%7D)
Taking natural logarithm on both sides we get,
![\ln (\frac{1}{2})=-0.0045(t)^{}](https://tex.z-dn.net/?f=%5Cln%20%28%5Cfrac%7B1%7D%7B2%7D%29%3D-0.0045%28t%29%5E%7B%7D)
![(-1)\ln (\frac{1}{2})=0.0045(t)](https://tex.z-dn.net/?f=%28-1%29%5Cln%20%28%5Cfrac%7B1%7D%7B2%7D%29%3D0.0045%28t%29)
![\ln (\frac{1}{2})^{-1}=0.0045(t)](https://tex.z-dn.net/?f=%5Cln%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-1%7D%3D0.0045%28t%29)
![\ln (2)=0.0045(t)](https://tex.z-dn.net/?f=%5Cln%20%282%29%3D0.0045%28t%29)
![0.6931=0.0045(t)](https://tex.z-dn.net/?f=0.6931%3D0.0045%28t%29)
![t=\frac{0.6931}{0.0045}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B0.6931%7D%7B0.0045%7D)
![t=154.02](https://tex.z-dn.net/?f=t%3D154.02)
Half-life of this substance is 154.02
c) To find the amount of substance will be present around in 2500 years
Put t=2500
we get,
![A=45e^{-0.0045(2500)}](https://tex.z-dn.net/?f=A%3D45e%5E%7B-0.0045%282500%29%7D)
![A=45e^{-11.25}](https://tex.z-dn.net/?f=A%3D45e%5E%7B-11.25%7D)
![A=45\times0.000013=0.000585](https://tex.z-dn.net/?f=A%3D45%5Ctimes0.000013%3D0.000585)
![A=0.000585](https://tex.z-dn.net/?f=A%3D0.000585)
The amount of substance will be present around in 2500 years is 0.000585 grams
Answer:
33 m/s
Step-by-step explanation:
120 km/h × (1 h)/(3600 s) × (1000 m)/(1 km) ≈ 33 m/s
_____
<em>Additional comment</em>
In general, units conversion is done by multiplying by a factor whose numerator and denominator have equal values, but different units. The units in that fraction need to be arranged to cancel the units you don't want and leave the units you do want.
Cost of goods = 1,500
Selling expense = 500
Total cost in selling = 1500 + 500 = 2000
Profit = Total Revenue - Total cost in selling = 3000 - 2000 = 1000
Profit = 1000
Hope this explains it.
Answer:
A
Step-by-step explanation:
Answers for A:
Factored form: (x-2)(x+4)
Zeros: x = 2, -4
Vertex: (-1, -9)
Answers for B:
Factored form: -(x+2)(x+7)
Zeros: x = -2, -7
Vertex: (-9/2, 25/4)