The decay factor here is 0.85, and it means the car’s value changes by 85% every year, or goes down by 15% every year.
The formula for exponential decay is y = a(1 - b)^x
y is the final amount.
a is the initial amount, which is $30,000 in this case.
(1 - b) is the decay factor, or the number the original value gets multiplied by each year, which is 0.85 here.
b is the percent decrease in decimal form. In this case, we can find it using the formula (1 - b) = 0.85. We soon find that b = 0.15, or 15%.
x is the number of years.
Answer:
The fifth root is 2[cos(56°) + i sin(56°)]
Step-by-step explanation:
* To solve this problem we must revise De Moiver's rule
- In the complex number with polar form
∵ z = r(cosФ + i sinФ)
∴ z^n = r^n(cos(nФ) + i sin(nФ))
* In the problem
- The fifth root means z^(1/5)
- We can put 32 as a form a^n
∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5
∴ z = 2^5[cos(280°) + i sin(280°)]
* Lets find z^(1/5)
![*z^{\frac{1}{5}}=[2^{5}]^{\frac{1}{5} } (cos(\frac{1}{5})(280)+isin(\frac{1}{5})(280)](https://tex.z-dn.net/?f=%2Az%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%3D%5B2%5E%7B5%7D%5D%5E%7B%5Cfrac%7B1%7D%7B5%7D%20%7D%20%28cos%28%5Cfrac%7B1%7D%7B5%7D%29%28280%29%2Bisin%28%5Cfrac%7B1%7D%7B5%7D%29%28280%29)

∴ z^(1/5) = 2[cos(56) + i sin(56)]
* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]
The answer to the question Is 19.8
V =πr^2h
v= 3.14×27×27×15
v=34335.9
v= 34336