Respuesta :
Answer:
t = -24*log(2/3)
Step-by-step explanation:
The expression is:
V = 22,500*10^(-t/12)
Replacing with V = 10,000 and isolating t, we get:
10,000 = 22,500*10^(-t/12)
10,000/22,500 = 10^(-t/12)
4/9 = 10^(-t/12)
(2/3)² = 10^(-t/12)
2*log(2/3) = -t/12
-12*2*log(2/3) = t
t = -24*log(2/3)
Answer:
The number of years after purchase at which Vishal's car will be worth $10,000 is [tex]Log_{10}\left (\frac{9}{4} \right )^{12}[/tex] years
Step-by-step explanation:
The relationship is given as follows
Value, V of the car = 22500×[tex]10^{-t/12}[/tex]
Therefore, when the car is $10,000 we will have
$10,000 = 22,500×[tex]10^{-t/12}[/tex]
Which will give;
[tex]\frac{10000}{22500} =\frac{4}{9} = 10^{-\frac{t}{12}}[/tex]
Hence;
[tex]Log\frac{4}{9} = Log(10^{-\frac{t}{12}} )[/tex]
Therefore;
[tex]-\frac{t}{12}\times Log_{10} 10 = Log\frac{4}{9}[/tex]
[tex]\because Log_{10} 10 = 1, \ we \ have; \ -\frac{t}{12} = Log_{10}\frac{4}{9}[/tex]
Which gives;
[tex]t = -12 \times Log_{10}\frac{4}{9} \ or \ t = Log_{10}\left (\frac{4}{9} \right )^{-12}[/tex]
[tex]\therefore t = Log_{10}\left (\frac{9}{4} \right )^{12}[/tex] years
Evaluated, the above equation becomes t = 4.226 years
Therefore, the number of years after purchase at which Vishal's car will be worth $10,000 = [tex]Log_{10}\left (\frac{9}{4} \right )^{12}[/tex] years.
