Answer:
The value of this investment at the end of the 5 years is of $662.5.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Dina invests $600 for 5 years at a rate of 2% per year compound interest.
This means that
. Thus
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
![A(t) = 600(1 + \frac{0.02}{1})^{t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20600%281%20%2B%20%5Cfrac%7B0.02%7D%7B1%7D%29%5E%7Bt%7D)
![A(t) = 600(1.02)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20600%281.02%29%5Et)
Calculate the value of this investment at the end of the 5 years.
This is A(5). So
![A(5) = 600(1.02)^5 = 662.5](https://tex.z-dn.net/?f=A%285%29%20%3D%20600%281.02%29%5E5%20%3D%20662.5)
The value of this investment at the end of the 5 years is of $662.5.
Answer:
9
Step-by-step explanation:
Answer:
the 3rd one and the last one
Step-by-step explanation:
functions can't have the same y coordinate.
<h2>
The required 'option C) 144' is correct.</h2>
Step-by-step explanation:
We have,
![(x^{\dfrac{1}{8}})(x^{\dfrac{3}{8}})=12](https://tex.z-dn.net/?f=%28x%5E%7B%5Cdfrac%7B1%7D%7B8%7D%7D%29%28x%5E%7B%5Cdfrac%7B3%7D%7B8%7D%7D%29%3D12)
To find, the possible value of x = ?
∴ ![(x^{\dfrac{1}{8}})(x^{\dfrac{3}{8}})=12](https://tex.z-dn.net/?f=%28x%5E%7B%5Cdfrac%7B1%7D%7B8%7D%7D%29%28x%5E%7B%5Cdfrac%7B3%7D%7B8%7D%7D%29%3D12)
⇒ ![x^{\dfrac{1}{8}+\dfrac{3}{8}}=12](https://tex.z-dn.net/?f=x%5E%7B%5Cdfrac%7B1%7D%7B8%7D%2B%5Cdfrac%7B3%7D%7B8%7D%7D%3D12)
Using the exponential identity,
![a^{m} a^{n} =a^{m+n}](https://tex.z-dn.net/?f=a%5E%7Bm%7D%20a%5E%7Bn%7D%20%3Da%5E%7Bm%2Bn%7D)
⇒ ![x^{\dfrac{1+3}{8}}=12](https://tex.z-dn.net/?f=x%5E%7B%5Cdfrac%7B1%2B3%7D%7B8%7D%7D%3D12)
⇒ ![x^{\dfrac{4}{8}}=12](https://tex.z-dn.net/?f=x%5E%7B%5Cdfrac%7B4%7D%7B8%7D%7D%3D12)
⇒ ![x^{\dfrac{1}{2}}=12](https://tex.z-dn.net/?f=x%5E%7B%5Cdfrac%7B1%7D%7B2%7D%7D%3D12)
Squaring both sides, we get
![(x^{\dfrac{1}{2}})^2=(12)^2](https://tex.z-dn.net/?f=%28x%5E%7B%5Cdfrac%7B1%7D%7B2%7D%7D%29%5E2%3D%2812%29%5E2)
⇒ ![x^{{\dfrac{1}{2}}\times2}=144](https://tex.z-dn.net/?f=x%5E%7B%7B%5Cdfrac%7B1%7D%7B2%7D%7D%5Ctimes2%7D%3D144)
⇒ x = 144
∴ The possible value of x = 144
Thus, the required 'option C) 144' is correct.