The table shows the number of people switching to a new telecommunications company over a 7-day period in August.

Question

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.

Answer 1

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