Question

A geometric sequence has an initial value of 1/2 and a common ratio of 8. Write an exponential function to represent this sequence.
A: f(X) = 8· (1/2)^x
B: f(X) = 8· (1/2)^-1
C: f(x) = 1/2 ·8^x
D: f(x) = 1/2 ·8^x-1

please help me

Answer 1

Answer:

The correct option is  D.

Step-by-step explanation:

It is given that the initial value of a GP is 1/2 and common ratio is 8. It means

$a_1=\frac{1}{2}$

$r=8$

The nth term of a GP is

$a_n=a_1r^{n-1}$

where, $a_1$ is inital value and r is common ratio.

Substitute $a_1=\frac{1}{2}$ and $r=8$ in the above formula.

$a_n=\frac{1}{2}(8)^{n-1}$

The exponential function to represent this sequence is

$f(x)=\frac{1}{2}(8)^{x-1}$

Therefore the correct option is D.

Answer 2

Answer:

D

Step-by-step explanation:

the n th term of a geometric sequence is

$a_{n}$ = a$r^{n-1}$

Where a is the first term and r the common ratio

here a = $\frac{1}{2}$ and r = 8, hence

f(x) = $\frac{1}{2}$$(8)^{x-1}$ → D