To find the correct exponential function for the given geometric sequence, we need to identify the initial term and the common ratio from the explicit formula.
The explicit formula for the geometric sequence is given as:
[tex]\[ f(n) = 1250(11)^{n-1} \][/tex]
The general form for a geometric sequence is:
[tex]\[ f(n) = a \cdot r^{n-1} \][/tex]
Here, we need to identify the values of [tex]\(a\)[/tex] and [tex]\(r\)[/tex] in the formula [tex]\( f(n) = 1250(11)^{n-1} \)[/tex]:
1. Initial Term (a):
The initial term [tex]\(a\)[/tex] is the coefficient of the [tex]\(11^{n-1}\)[/tex] term. So, [tex]\( a = 1250 \)[/tex].
2. Common Ratio (r):
The common ratio [tex]\(r\)[/tex] is the base of the exponential term with the power [tex]\(n-1\)[/tex]. Here [tex]\( r = 11 \)[/tex].
Using these values in the general form, the exponential function can be written as:
[tex]\[ f(n) = \frac{1250}{1}(11)^{n-1} \][/tex]
Thus, the correct exponential function is:
[tex]\[ f(n) = \frac{1250}{1}(11)^{n-1} \][/tex]
