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)
Let
x----------> number of weeks
y----------> saved money
we now that
<span>Michael begins with $20 and saves $5 per week
so
y=20+5x------> equation 1
and
</span><span>Lindsey begins with no money, but saves $10 per week
</span><span>y=10x-------> equation 2
</span><span>the number of weeks it will take for Lindsey and Michael to save the same amount of money is when equation 1 is equals to equation 2
</span>
therefore
20+5x=10x------> 10x-5x=20------> 5x=20-----> x=20/5-----> x=4 weeks
the answer is
4 weeks
Answer:
241/20
Step-by-step explanation:
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