Using an exponential function, it is found that it takes 5.42 years for the car to halve in value.
<h3>What is an exponential function?</h3>
A decaying exponential function is modeled by:
![A(t) = A(0)(1 - r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%20-%20r%29%5Et)
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem, the car depreciates 12% a year in value, hence r = 0.12 and the equation is given by:
.
It halves in value at t years, for which A(t) = 0.5A(0), hence:
![A(t) = A(0)(0.88)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.88%29%5Et)
![0.5A(0) = A(0)(0.88)^t](https://tex.z-dn.net/?f=0.5A%280%29%20%3D%20A%280%29%280.88%29%5Et)
![(0.88)^t = 0.5](https://tex.z-dn.net/?f=%280.88%29%5Et%20%3D%200.5)
![\log{(0.88)^t} = \log{0.5}](https://tex.z-dn.net/?f=%5Clog%7B%280.88%29%5Et%7D%20%3D%20%5Clog%7B0.5%7D)
![t\log{0.88} = \log{0.5}](https://tex.z-dn.net/?f=t%5Clog%7B0.88%7D%20%3D%20%5Clog%7B0.5%7D)
![t = \frac{\log{0.5}}{\log{0.88}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B0.5%7D%7D%7B%5Clog%7B0.88%7D%7D)
t = 5.42.
It takes 5.42 years for the car to halve in value.
More can be learned about exponential functions at brainly.com/question/25537936
#SPJ1
Answer:
Step-by-step explanation:
πx=−2x2+6x−9 has (A) no solution (B) one solution (C) two solutions (D) infinite solutions
Answer:
--3 ±sqrt((-3)^2 -4(4)(-9))
-------------------------------
2(4)
Step-by-step explanation:
4x^2-5=3x+4
We need to get this in standard form to answer the question
Subtract 3x from each side
4x^2-3x-5=3x-3x+4
4x^2-3x-5=+4
Subtract 4 from each side
4x^2-3x-9 =0
a = 4
b = -3
c = -9
-b ±sqrt(b^2 -4ac)
---------------------------
2a
--3 ±sqrt((-3)^2 -4(4)(-9))
-------------------------------
2(4)
Answer:
d. 13.5, 20.25
Step-by-step explanation:
An exponential function is monotonic and does not change sign. On this basis alone, the first three choices can be eliminated.
The common ratio is 6/4 = 3/2.
The term in the sequence after 9 is 9·(3/2) = 27/2 = 13.5.
The term in the sequence after 27/2 is (27/2)·(3/2) = 81/4 = 20.25.
Answer:
b c e
Step-by-step explanation: