Answer:
Compound Interest,I- ![I=P[(1+I)^{4.5}-1]](https://tex.z-dn.net/?f=I%3DP%5B%281%2BI%29%5E%7B4.5%7D-1%5D)
Total Amount, A- ![A=P(1+i)^{4.5}](https://tex.z-dn.net/?f=A%3DP%281%2Bi%29%5E%7B4.5%7D)
Step-by-step explanation:
Compound interest is the difference between the initial amount invested at time t=0and the final amount of the investment at time t.
-Let the initial amount invested be P, the annual rate be i and A be the final amount of the investment.
-Let I be the compound interest earned.
-Given that the investment term n=4yrs 6 months, the compound interest is calculated as;
![A=P(1+i)^n\\\\I=A-P\\\\\# n=4.5,P=P, i=i\\\\\therefore I=P(1+i)^{4.5}-P\\\\=P[(1+I)^{4.5}-1]\\\\I=P[(1+I)^{4.5}-1]](https://tex.z-dn.net/?f=A%3DP%281%2Bi%29%5En%5C%5C%5C%5CI%3DA-P%5C%5C%5C%5C%5C%23%20n%3D4.5%2CP%3DP%2C%20i%3Di%5C%5C%5C%5C%5Ctherefore%20I%3DP%281%2Bi%29%5E%7B4.5%7D-P%5C%5C%5C%5C%3DP%5B%281%2BI%29%5E%7B4.5%7D-1%5D%5C%5C%5C%5CI%3DP%5B%281%2BI%29%5E%7B4.5%7D-1%5D)
Hence, the compound interest after 4 1/2 years is ![I=P[(1+I)^{4.5}-1]](https://tex.z-dn.net/?f=I%3DP%5B%281%2BI%29%5E%7B4.5%7D-1%5D)
#The total amount after the same period is ![A=P(1+i)^{4.5}](https://tex.z-dn.net/?f=A%3DP%281%2Bi%29%5E%7B4.5%7D)
4w-7k=28
Move variable to the right to get -7k=28-4w
Divide both sides by -7
k= -4+4/7w
Answer:
6:1
Step-by-step explanation:
1.8:0.3
each times by 10
18:3
each divided by 3
6:1
An exponent signifies repeated multiplication.
the factor x is repeated 3 times
Exponents can be added and subtracted to express the effects of multiplication and division.
![\dfrac{x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}=\dfrac{x^{5}}{x^{3}}\\\\=\dfrac{x\cdot x\cdot x}{x\cdot x\cdot x}\cdot x\cdot x=x\cdot x\\\\=x^{(5-3)}=x^{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5Ccdot%20x%5Ccdot%20x%5Ccdot%20x%5Ccdot%20x%7D%7Bx%5Ccdot%20x%5Ccdot%20x%7D%3D%5Cdfrac%7Bx%5E%7B5%7D%7D%7Bx%5E%7B3%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bx%5Ccdot%20x%5Ccdot%20x%7D%7Bx%5Ccdot%20x%5Ccdot%20x%7D%5Ccdot%20x%5Ccdot%20x%3Dx%5Ccdot%20x%5C%5C%5C%5C%3Dx%5E%7B%285-3%29%7D%3Dx%5E%7B2%7D)
The addition and subtraction of exponents works the same even when there are more denominator factors than numerator factors.
![\dfrac{x\cdot x\cdot x}{x\cdot x\cdot x\cdot x\cdot x}=\dfrac{x^{3}}{x^{5}}=\dfrac{1}{x^{2}}\\\\=x^{(3-5)}=x^{-2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5Ccdot%20x%5Ccdot%20x%7D%7Bx%5Ccdot%20x%5Ccdot%20x%5Ccdot%20x%5Ccdot%20x%7D%3D%5Cdfrac%7Bx%5E%7B3%7D%7D%7Bx%5E%7B5%7D%7D%3D%5Cdfrac%7B1%7D%7Bx%5E%7B2%7D%7D%5C%5C%5C%5C%3Dx%5E%7B%283-5%29%7D%3Dx%5E%7B-2%7D)
That is, a negative numerator exponent is the same as a positive denominator exponent and vice versa. You can move a factor with an exponent from denominator to numerator and change the sign of the exponent, and vice versa.
Your expression has 3 in the denominator with a negative exponent. It can be moved to the numerator and the exponent changed to positive:
![\dfrac{1}{3^{-2}}=3^{2}\\\\=3\cdot 3=\bf{9}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B3%5E%7B-2%7D%7D%3D3%5E%7B2%7D%5C%5C%5C%5C%3D3%5Ccdot%203%3D%5Cbf%7B9%7D)