Answer:
Step-by-step explanation:
Perhaps you want to use the points (t, P) = (4, 150) and (6, 160) to find the parameters P0 and k in the equation ...
![P(t)=P_0\cdot e^{kt}](https://tex.z-dn.net/?f=P%28t%29%3DP_0%5Ccdot%20e%5E%7Bkt%7D)
We know from the given points that we can write the equation as ...
![P(t)=150\left(\dfrac{160}{150}\right)^{(t-4)/(6-4)}=150\left(\dfrac{16}{15}\right)^{\frac{t}{2}-2}\\\\=150\left(\dfrac{16}{15}\right)^{-2}\times\left(\left(\dfrac{16}{15}\right)^{\frac{1}{2}}\right)^t](https://tex.z-dn.net/?f=P%28t%29%3D150%5Cleft%28%5Cdfrac%7B160%7D%7B150%7D%5Cright%29%5E%7B%28t-4%29%2F%286-4%29%7D%3D150%5Cleft%28%5Cdfrac%7B16%7D%7B15%7D%5Cright%29%5E%7B%5Cfrac%7Bt%7D%7B2%7D-2%7D%5C%5C%5C%5C%3D150%5Cleft%28%5Cdfrac%7B16%7D%7B15%7D%5Cright%29%5E%7B-2%7D%5Ctimes%5Cleft%28%5Cleft%28%5Cdfrac%7B16%7D%7B15%7D%5Cright%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Cright%29%5Et)
Comparing this to the desired form, we see that ...
![P_0=150\left(\dfrac{16}{15}\right)^{-2}\approx 131.836\\\\e^{k}=\left(\dfrac{16}{15}\right)^{1/2}\rightarrow k=\dfrac{1}{2}(\ln{16}-\ln{15})\approx 0.0322693](https://tex.z-dn.net/?f=P_0%3D150%5Cleft%28%5Cdfrac%7B16%7D%7B15%7D%5Cright%29%5E%7B-2%7D%5Capprox%20131.836%5C%5C%5C%5Ce%5E%7Bk%7D%3D%5Cleft%28%5Cdfrac%7B16%7D%7B15%7D%5Cright%29%5E%7B1%2F2%7D%5Crightarrow%20k%3D%5Cdfrac%7B1%7D%7B2%7D%28%5Cln%7B16%7D-%5Cln%7B15%7D%29%5Capprox%200.0322693)
So, the approximate equation for P is ...
![P(t)=131.836\cdote^{0.032t}](https://tex.z-dn.net/?f=P%28t%29%3D131.836%5Ccdote%5E%7B0.032t%7D)
And the parameters of interest are ...
Answer:
![f^{-1}(x) = \frac{x+8}{8}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Cfrac%7Bx%2B8%7D%7B8%7D)
Domain of f(x): All real values.
Range of f(x): All real values.
Domain of f -1(x): All real values.
Range of f -1(x): All real values
Step-by-step explanation:
We are given the following function:
![f(x) = 8x + 8](https://tex.z-dn.net/?f=f%28x%29%20%3D%208x%20%2B%208)
Since it is a line, we have that both the domain is the range is the real set.
Inverse function:
The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.
Finding the inverse function:
Exchange x and y in the original function, and isolate y. So
Original
![y = 8x + 8](https://tex.z-dn.net/?f=y%20%3D%208x%20%2B%208)
Exchanging:
![x = 8y - 8](https://tex.z-dn.net/?f=x%20%3D%208y%20-%208)
Isolating y:
![8y = x + 8](https://tex.z-dn.net/?f=8y%20%3D%20x%20%2B%208)
![y = \frac{x+8}{8}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Bx%2B8%7D%7B8%7D)
![f^{-1}(x) = \frac{x+8}{8}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Cfrac%7Bx%2B8%7D%7B8%7D)
Answer:
$909.50
Step-by-step explanation:
$850 x 7% = $59.50 (tax amount)
850 x (1+ 0.07) = $909.50
Hi,
Let the
Youngest brothers age = x+2
Middle brothers age = x+4
Oldest brothers age = x+6
So,
Youngest brothers age = x+2 = 28+2 = 30 years of age
Middle brothers age = x+4 = 28+4 = 32 years of age
Oldest brothers age = x+6 = 28+6 = 34 years of age
Have a great day!
Answer:
5z
Step-by-step explanation:
3z+5z-3z(3z gets cancelled)
5z