We're given the following function:
![f(x)=log(.75^x)=log[ (\frac{3}{4}) ^{x}]=log( \frac{3^x}{4^x})](https://tex.z-dn.net/?f=f%28x%29%3Dlog%28.75%5Ex%29%3Dlog%5B%20%20%28%5Cfrac%7B3%7D%7B4%7D%29%20%5E%7Bx%7D%5D%3Dlog%28%20%5Cfrac%7B3%5Ex%7D%7B4%5Ex%7D%29%20%20)
In order to see if the function is decreasing we'll take its derivative. If
the function is increasing, if
the function is decreasing.
We take the derivate:
![\frac{d}{dx}[log( \frac{3^x}{4^x})]= \frac{4^x}{3^x}[ \frac{d}{dx} (\frac{3^x}{4^x})]=\frac{4^x}{3^x} \frac{4^x[ \frac{d}{dx} (3^x)]-3^x[ \frac{d}{dx} (4^x)]}{ 4^2^x}=](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5Blog%28%20%5Cfrac%7B3%5Ex%7D%7B4%5Ex%7D%29%5D%3D%20%5Cfrac%7B4%5Ex%7D%7B3%5Ex%7D%5B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%28%5Cfrac%7B3%5Ex%7D%7B4%5Ex%7D%29%5D%3D%5Cfrac%7B4%5Ex%7D%7B3%5Ex%7D%20%5Cfrac%7B4%5Ex%5B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%283%5Ex%29%5D-3%5Ex%5B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%284%5Ex%29%5D%7D%7B%204%5E2%5Ex%7D%3D)
![\frac{4^x}{3^x} \frac{4^x[3^xlog(3)]-3^x[4^x[4^xlog(4)]}{ 4^2^x}=log(3)-log(4)\ \textless \ 0](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Ex%7D%7B3%5Ex%7D%20%5Cfrac%7B4%5Ex%5B3%5Exlog%283%29%5D-3%5Ex%5B4%5Ex%5B4%5Exlog%284%29%5D%7D%7B%204%5E2%5Ex%7D%3Dlog%283%29-log%284%29%5C%20%5Ctextless%20%5C%200)
Which implies the function is decreasing.
Another way to answer the problem (although less insightful) you can take any two real numbers
and
such that
, then if
the function is increasing and if
the function is decreasing. You can verify the function is decreasing with any two numbers in the function's domain.
The modal and mean mark of the frequency distribution is 5 and 4.83 respectively.
<h3>Mean and mode</h3>
Mode refers to a mark which reoccurs most in a frequency distribution.
The total number of students who wrote the test = 2 + 3 + 4 + 6 + 10 + 4 + 3 + 2 + 1 + 1
= 36 students
Mean mark = Total mark / Total students
= (2×1) + (3×2) + (4×3) + (6×4) + (10×5) + (4×6) + (3×7) + (2×8) + (1×9) + (1×10) / 36
= (2+6+12+24+50+24+21+16+9+10 / 36
= 174/36
= 4.83333333333333
Approximately,
Mean mark = 4.83
If 25% of students failed,
Number of students who failed = 25% of 36
= 25/100 × 36
= 0.25 × 36
= 9 students.
Learn more about mean and mode:
brainly.com/question/14532771
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Answer:
£14889.30
Step-by-step explanation:
The cost of the car = £15500.
For the first year,
depreciation = £15500 x 1%
= £155
Its worth after the first year = £15500 - £155
= £15345
For the 2nd year,
depreciation = £15345 x 1%
= £153.45
Its worth after the second year = £15345 - £153.45
= £15191.55
For the 3rd year,
depreciation = £15191.55 x 1%
= £151.9155
Its worth after the third year = £15191.55 - £151.9155
= £15039.6345
For the 4th year,
depreciation = £15039.6345 x 1%
= £150.3963
Its worth after the fourth year = £15039.6345 - £150.3963
= £14889.2382
Thus, the worth of the car in 4 years would be £14889.30
Answer:
∠ ABC = 90°
Step-by-step explanation:
∠ ABC is the angle in a semi circle and is right, that is
∠ ABC = 90°
Answer:
Divide.....
Step-by-step explanation:
I would like to have an apple though xD
