Answer:
Starting point is (0, 210).
Rate of change is 0.12 or 12%.
Step-by-step explanation:
Given:
The given function is:
[tex]a(x)=210(1.12)^x[/tex]
The above function represents an exponential growth function of the form:
[tex]a(x)=a_0(1+r)^x\\Where,\ a(x)\rightarrow \textrm{Value after a given quantity of x}\\a_0\rightarrow \textrm{Initial value or Starting value when 'x' is 0.}\\r\rightarrow \textrm{Rate of change of the value}\\x\rightarrow \textrm{The variable on which the value 'a' depends}[/tex]
Now, we need to convert the given function in the standard form.
So, we write 1.12 as sum of 1 and a number.
So, 1.12 = 1 + 0.12
Therefore, the given function can be rewritten as:
[tex]a(x)=210(1+0.12)^x[/tex]
Now, on comparing it with the general form, we conclude:
[tex]a_0=210\\r=0.12[/tex]
Therefore, the rate of change is 0.12 or 12 %.
Also, the starting point on the graph will be when 'x' is 0. So, the starting point is (0,210).
