Answer:
Step-by-step explanation:
common factor of 2a² and 10ab= 2a
With annual compounding, the value of the investment after 7 years is
Value = $3,000 [ 1 + 0.05 ] to the 7th power .
Value = $3,000 [ 1.4071 ] = <u>$4,221.30</u>
Answer:
Step-by-step explanation:
The equation for the amount of money in an account after a certain amount is deposited and compounded after t years once per year is
![A(t)=P(1+r)^t](https://tex.z-dn.net/?f=A%28t%29%3DP%281%2Br%29%5Et)
Our A(t) = 33800, P = 4400, r = .075 and we are looking for t. Filling in:
and
![33800=4400(1.075)^t](https://tex.z-dn.net/?f=33800%3D4400%281.075%29%5Et)
Begin by dividing both sides by 4400 to get
![7.681818182=1.075^t](https://tex.z-dn.net/?f=7.681818182%3D1.075%5Et)
The only way to move that t our from its current position as an exponent is to take the natural log of both sides and follow the rules for natural logs:
![ln(7.6181818182=ln(1.075)^t](https://tex.z-dn.net/?f=ln%287.6181818182%3Dln%281.075%29%5Et)
The power rule of natural logs says we can move that exponent down in front, giving us:
![ln(7.681818182)=t*ln(1.075)](https://tex.z-dn.net/?f=ln%287.681818182%29%3Dt%2Aln%281.075%29)
Divide both sides by ln(1.075) to get
![\frac{ln(7.61818182)}{ln(1.075)} =t](https://tex.z-dn.net/?f=%5Cfrac%7Bln%287.61818182%29%7D%7Bln%281.075%29%7D%20%3Dt)
Do this division on your calculator to get
t = 28.2 years
Answer: y = -4x + 18
Both equations have the same slope.
y = -4x + b
x = 3
y = 6
6 = -4(3) + b
6 = -12 + b
6 + 12 = b