Answer:
Final answer is approx 6.644 years.
Step-by-step explanation:
Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.
So we can use growth formula:
![A=P\left(1+r\right)^t](https://tex.z-dn.net/?f=A%3DP%5Cleft%281%2Br%5Cright%29%5Et)
Then we get equation for motorcycles and cars as:
![A=5.75\left(1+0.16\right)^t](https://tex.z-dn.net/?f=A%3D5.75%5Cleft%281%2B0.16%5Cright%29%5Et)
![A=3.5\left(1+0.25\right)^t](https://tex.z-dn.net/?f=A%3D3.5%5Cleft%281%2B0.25%5Cright%29%5Et)
Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:
![3.5\left(1+0.25\right)^t>5.75\left(1+0.16\right)^t](https://tex.z-dn.net/?f=3.5%5Cleft%281%2B0.25%5Cright%29%5Et%3E5.75%5Cleft%281%2B0.16%5Cright%29%5Et)
![3.5\left(1.25\right)^t>5.75\left(1.16\right)^t](https://tex.z-dn.net/?f=3.5%5Cleft%281.25%5Cright%29%5Et%3E5.75%5Cleft%281.16%5Cright%29%5Et)
![3.5\left(1.25\right)^t>5.75\left(1.16\right)^t](https://tex.z-dn.net/?f=3.5%5Cleft%281.25%5Cright%29%5Et%3E5.75%5Cleft%281.16%5Cright%29%5Et)
![\frac{\left(1.25\right)^t}{\left(1.16\right)^t}>\frac{5.75}{3.5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%281.25%5Cright%29%5Et%7D%7B%5Cleft%281.16%5Cright%29%5Et%7D%3E%5Cfrac%7B5.75%7D%7B3.5%7D)
![\left(\frac{1.25}{1.16}\right)^t>1.64285714286](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7B1.25%7D%7B1.16%7D%5Cright%29%5Et%3E1.64285714286)
![t\cdot\ln\left(\frac{1.25}{1.16}\right)>\ln\left(1.64285714286\right)](https://tex.z-dn.net/?f=t%5Ccdot%5Cln%5Cleft%28%5Cfrac%7B1.25%7D%7B1.16%7D%5Cright%29%3E%5Cln%5Cleft%281.64285714286%5Cright%29)
![t>\frac{\ln\left(1.64285714286\right)}{\ln\left(\frac{1.25}{1.16}\right)}](https://tex.z-dn.net/?f=t%3E%5Cfrac%7B%5Cln%5Cleft%281.64285714286%5Cright%29%7D%7B%5Cln%5Cleft%28%5Cfrac%7B1.25%7D%7B1.16%7D%5Cright%29%7D)
![t>6.6436473051](https://tex.z-dn.net/?f=t%3E6.6436473051)
Hence final answer is approx 6.644 years.
Answer:
D. The graph of function
is the graph of function
shifted 4 units to the left.
Step-by-step explanation:
the function
is composite function between
and
, then you can re-write
as:
![g(x) = 10^{x+4}](https://tex.z-dn.net/?f=g%28x%29%20%3D%2010%5E%7Bx%2B4%7D)
The transformation happened in the input, then you have an horizontal shifted and how it's adding 4 units then you go "faster" and move to left the graph.
In the image you can see what's mean sum a constant in the
of a function.
Answer:
yoo thanks u the goat
Step-by-step explanation:
0.1 or 1/10 is in simplest form