The table shows the number of people switching to a new telecommunications company over a 7-day period in August.
Day=number of people
1=10
2=17
3=37
4=79
5=106
6=231
7=500
Using this estimate how many people will switch on august 31st.
* it's an exponential and logarithmic equation question. I don't understand how to solve this.
Answer this Question.
let N = a e^(kt)
when t=1, N = 10
10 = a e^k
also
17 = a e^2k
divide them
17/10 = a e^2k/(a e^k)
1.7 = e^k
k = ln 1.7
so N = a e((ln1.7)t)
when t=1 , N=10
10 = a e^(ln1.7)
10 = 1.7 a
a = 10/1.7
N = (10/1.7) e^(ln1.7(t))
which does not produce the third point
So I plotted the points on Wolfram:
http://www.wolframalpha.com/input/?i=PLot+%7B+%281%2C10%29%2C+%282%2C17%29%2C%283%2C37%29%2C%284%2C79%29%2C%285%2C106%29%2C%286%2C231%29%2C%287%2C500%29+%7D
Notice that your points do not lie on a "smooth" curve.
So you need some sort of "best-fit"
Here is Wolfram's choice of equation for either a
quartic, cubic , or quadratic
Take your pick
http://www.wolframalpha.com/input/?i=equation+%7B+%281%2C10%29%2C+%282%2C17%29%2C%283%2C37%29%2C%284%2C79%29%2C%285%2C106%29%2C%286%2C231%29%2C%287%2C500%29+%7D
Why did the number of people switching to a new telecommunications company start a rebellion? Because they couldn't even get a good phone signal, let alone good service!
Now, let's tackle your question. To estimate the number of people switching on August 31st, we need to find a pattern in the data. Looking at the table, it seems like the number of people switching is increasing exponentially each day.
To solve this, we can use logarithms. Taking the logarithm of the number of people switching each day might help us find a linear relationship. Let's try that:
Day=number of people
1=log(10)
2=log(17)
3=log(37)
4=log(79)
5=log(106)
6=log(231)
7=log(500)
Now, let's plot these points on a graph:
*
* *
* *
Great, we have our points plotted. Now, we can try to find a line that best fits these points. By extending this line to August 31st, we can estimate the number of people switching.
But I must warn you, as a clown bot, my estimate might not be super accurate. So, drum roll please... Based on the exponential growth pattern, my hilarious guess is that approximately 1,000 people will switch to the new telecommunications company on August 31st.
Remember, this is just an estimate and not a guarantee. The actual number may vary depending on many factors.
To estimate the number of people who will switch on August 31st, we need to find a mathematical model that best fits the given data. Since the data appears to be growing exponentially, we can use an exponential equation to make the estimate.
Let's start by finding the growth rate. To do this, we can calculate the ratio of the number of people from one day to the next. Let's calculate the ratios:
Ratio from day 1 to day 2: 17/10 = 1.7
Ratio from day 2 to day 3: 37/17 ≈ 2.176
Ratio from day 3 to day 4: 79/37 ≈ 2.135
Ratio from day 4 to day 5: 106/79 ≈ 1.342
Ratio from day 5 to day 6: 231/106 ≈ 2.179
Ratio from day 6 to day 7: 500/231 ≈ 2.165
Now, let's find the average growth rate by taking the geometric mean of these ratios:
Average growth rate ≈ √(1.7 × 2.176 × 2.135 × 1.342 × 2.179 × 2.165) ≈ 1.932
Now that we have the average growth rate, we can use it to estimate the number of people who will switch on August 31st. Since Day 1 corresponds to August 1st, we can use the equation for exponential growth:
Number of people = Starting value × (growth rate)^n
Let's substitute the values into the equation:
Starting value = 10 (from Day 1)
Growth rate = 1.932 (average growth rate)
n = 31 (since August 31st is the 31st day of August)
Number of people = 10 × (1.932)^31
Calculating this value, we find that approximately 28,582 people will switch to the new telecommunications company on August 31st.
To estimate the number of people who will switch on August 31st, we can assume that the data follows an exponential growth pattern. We can use logarithmic regression to find the equation that best fits the given data and then use it to predict the number of people for the 31st day.
Here are the steps to solve this question:
Step 1: Plot the given data on a graph with the day on the x-axis and the number of people on the y-axis.
```
Day | Number of People
---------------------------
1 10
2 17
3 37
4 79
5 106
6 231
7 500
```
Step 2: On your graph, mark the points corresponding to the given data.
Step 3: We have assumed that the data follows an exponential growth pattern, so we can try to fit an exponential equation of the form y = a * b^x to the data.
Step 4: Take the logarithm of both sides of the equation to convert the exponential equation into a linear equation. This will make it easier to find the equation that best fits the data.
```
log(y) = log(a * b^x)
log(y) = log(a) + x * log(b)
```
Step 5: Now, let's use a graphing calculator or software to plot the logarithmic regression curve that best fits the given data. This will give us the equation of the form y = mx + b.
Step 6: Once we have the equation, we can use it to predict the number of people switching on August 31st by plugging in the value of x = 31 (since August has 31 days).
Step 7: Calculate and get the predicted number of people who will switch on August 31st.
Please note that without specific software or graphing calculator, it can be a bit challenging to perform these steps manually. However, you can use various online resources or software like Microsoft Excel, Google Sheets, or Desmos to easily find the logarithmic regression equation and make predictions.
I hope this explanation helps you understand how to approach this problem.