Your answer will be 560,000 because you convert 10% to a decimal which is .10 and times .10 by 56,000 and you get your answer 560,000
The car can travel 1120 miles because 20 times 56 equals 1120
= ![\frac{5}{7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B7%7D%20%20)
Cross multiply. (7)(x) = (5)(x - 2)
7x = 5x - 10
Subtract 5x from both sides.
2x = -10
Divide both sides by 2.
x = -5
Answer: After 18.05 minutes, the temperature of steel becomes 100 degrees.
Step-by-step explanation:
Since we have given that
Initial temperature = 2500
At t = 0,
we get that
![f(t)=Ce^{-kt}+80\\\\2500=C+80\\\\2500-80=C\\\\2420=C](https://tex.z-dn.net/?f=f%28t%29%3DCe%5E%7B-kt%7D%2B80%5C%5C%5C%5C2500%3DC%2B80%5C%5C%5C%5C2500-80%3DC%5C%5C%5C%5C2420%3DC)
After 2 minutes, the temperature of the steel is 1500 degrees.
so, it becomes,
![1500=2420e^{-2k}+80\\\\1500-80=2420e^{-2k}\\\\\dfrac{1420}{2420}=e^{-2k}\\\\0.587=e^{-2k}\\\\\ln 0.587=-2k\\\\-0.533=-2k\\\\k=\dfrac{0.533}{2}\\\\k=0.266](https://tex.z-dn.net/?f=1500%3D2420e%5E%7B-2k%7D%2B80%5C%5C%5C%5C1500-80%3D2420e%5E%7B-2k%7D%5C%5C%5C%5C%5Cdfrac%7B1420%7D%7B2420%7D%3De%5E%7B-2k%7D%5C%5C%5C%5C0.587%3De%5E%7B-2k%7D%5C%5C%5C%5C%5Cln%200.587%3D-2k%5C%5C%5C%5C-0.533%3D-2k%5C%5C%5C%5Ck%3D%5Cdfrac%7B0.533%7D%7B2%7D%5C%5C%5C%5Ck%3D0.266)
So, We need to find the number of minutes when the temperature of steel would be 100 degrees.
So, it becomes,
![100=2420e^{-0.266t}+80\\\\100-80=2420e^{-0.266t}\\\\20=2420e^{-0.266t}\\\\\dfrac{20}{2420}=e^{-0.266t}\\\\\ln \dfrac{20}{2420}=-0.266t\\\\-4.8=-0.266t\\\\t=\dfrac{4.8}{0.266}\\\\t=18.05](https://tex.z-dn.net/?f=100%3D2420e%5E%7B-0.266t%7D%2B80%5C%5C%5C%5C100-80%3D2420e%5E%7B-0.266t%7D%5C%5C%5C%5C20%3D2420e%5E%7B-0.266t%7D%5C%5C%5C%5C%5Cdfrac%7B20%7D%7B2420%7D%3De%5E%7B-0.266t%7D%5C%5C%5C%5C%5Cln%20%5Cdfrac%7B20%7D%7B2420%7D%3D-0.266t%5C%5C%5C%5C-4.8%3D-0.266t%5C%5C%5C%5Ct%3D%5Cdfrac%7B4.8%7D%7B0.266%7D%5C%5C%5C%5Ct%3D18.05)
Hence, after 18.05 minutes, the temperature of steel becomes 100 degrees.
Compare to slope intercept form of line y=mx+b
- Rate of change=m=-9
- Y intercept=b=55000
Initial value is 55000