Answer:
C. ![N(t)=150\cdot 3^t](https://tex.z-dn.net/?f=N%28t%29%3D150%5Ccdot%203%5Et)
Step-by-step explanation:
You are given the exponential function ![n(t)=ab^t.](https://tex.z-dn.net/?f=n%28t%29%3Dab%5Et.)
From the table,
at
thus
![N(0)=a\cdot b^0\\ \\150=a\cdot 1\ [\text{ because }b^0=1]](https://tex.z-dn.net/?f=N%280%29%3Da%5Ccdot%20b%5E0%5C%5C%20%5C%5C150%3Da%5Ccdot%201%5C%20%5B%5Ctext%7B%20because%20%7Db%5E0%3D1%5D)
Also
at
thus
![N(1)=a\cdot b^1=a\cdot b.](https://tex.z-dn.net/?f=N%281%29%3Da%5Ccdot%20b%5E1%3Da%5Ccdot%20b.)
Since
substitute it into the second equation
![450=150\cdot b\\ \\b=\dfrac{450}{150}\\ \\b=3](https://tex.z-dn.net/?f=450%3D150%5Ccdot%20b%5C%5C%20%5C%5Cb%3D%5Cdfrac%7B450%7D%7B150%7D%5C%5C%20%5C%5Cb%3D3)
and the expression for the exponential function is
![N(t)=150\cdot 3^t](https://tex.z-dn.net/?f=N%28t%29%3D150%5Ccdot%203%5Et)
<h3>
The monthly cost of cell phone is A = 40 + 0.005 m</h3>
Step-by-step explanation:
The monthly fixed charges by mobile company = $40
The cost of sending each text message = 0.05 cents
Now, 100 cents = 1 dollar
⇒ 1 cent =$ ![(\frac{1}{100} )](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B100%7D%20%29)
⇒ 0.05 cent s =$ ![(\frac{1}{100} \times 0.05) =0.0005](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B100%7D%20%20%5Ctimes%200.05%29%20%20%3D0.0005)
Also, the number of text messages send = m
So, the cost of sending m text message = m x ( cost of 1 text )
= m x ( $ 0.0005) = 0.0005 m
Now, Total bill = Fixed rate + cost of m texts
⇒ A =$40 + $ 0.0005 m
Hence, the monthly cost of cell phone is A = 40 + 0.005 m
Answer:
midpoint equation
Step-by-step explanation: