Answer:
60, if they all have the same age, 60 * 3 = 180.
The oldest one has to be aged 60 along with the youngest aged.
Answer:
The slope is undefined.
Step-by-step explanation:
You can use slope formula (y - y)/(x - x) and you will get a zero on the bottom (never allowed) OR notice that the x's are the same so sketch a graph, the line is vertical...that means that slope is undefined.
An exponential function is given by
![y=a(b)^x](https://tex.z-dn.net/?f=y%3Da%28b%29%5Ex)
Given two points, (m, n) and (p, q), we find the equation of the exponential function as follows:
![n=a(b)^m \ .\ .\ .\ (1) \\ \\ q=a(b)^p \ .\ .\ .\ (2) \\ \\ \frac{(1)}{(2)} \Rightarrow \frac{n}{q} = \frac{b^m}{b^p} =b^{m-p} \\ \\ \Rightarrow \ln\left( \frac{n}{q} \right)=(m-p)\ln(b) \\ \\ \Rightarrow \ln(b)= \frac{\ln\left( \frac{n}{q} \right)}{m-p} \\ \\ \Rightarrow b=e^{\frac{\ln\left( \frac{n}{q} \right)}{m-p}](https://tex.z-dn.net/?f=n%3Da%28b%29%5Em%20%5C%20.%5C%20.%5C%20.%5C%20%281%29%20%5C%5C%20%20%5C%5C%20q%3Da%28b%29%5Ep%20%5C%20.%5C%20.%5C%20.%5C%20%282%29%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B%281%29%7D%7B%282%29%7D%20%5CRightarrow%20%5Cfrac%7Bn%7D%7Bq%7D%20%3D%20%5Cfrac%7Bb%5Em%7D%7Bb%5Ep%7D%20%3Db%5E%7Bm-p%7D%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%3D%28m-p%29%5Cln%28b%29%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Cln%28b%29%3D%20%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%20%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20b%3De%5E%7B%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D)
From (1), we have:
![n=a\left(e^{m\frac{\ln\left( \frac{n}{q} \right)}{m-p}\right) \\ \\ \Rightarrow a= \frac{n}{\left(e^{m\frac{\ln\left( \frac{n}{q} \right)}{m-p}\right)}}](https://tex.z-dn.net/?f=n%3Da%5Cleft%28e%5E%7Bm%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%5Cright%29%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20a%3D%20%5Cfrac%7Bn%7D%7B%5Cleft%28e%5E%7Bm%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%5Cright%29%7D%7D)
Therefore, the equation of an exponential function given two points (m, n) and (p, q) is given by
![y=\frac{n}{\left(e^{m\frac{\ln\left( \frac{n}{q} \right)}{m-p}\right)}}\left(e^{\frac{\ln\left( \frac{n}{q} \right)}{m-p}\right)^x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bn%7D%7B%5Cleft%28e%5E%7Bm%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%5Cright%29%7D%7D%5Cleft%28e%5E%7B%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%5Cright%29%5Ex)
[i.e. you can choose any set of points and substitute the values in the equation above to get the exponential equation]
Answer:
Estimation: 12900
Exact Number: 12913
Step-by-step explanation:
5673 → 5700
4811 → 4800
2429 → 2400
_____ _____
12913 12900
Round to the nearest hundred in this case.
I am joyous to assist you anytime.
They played 6 songs between their first and second break.