Answer :
Answer:
The first term is 81.
The second term is 27 (which is obtained by multiplying the previous term by (1/3)).
The third term is 9 (which is obtained by multiplying the second term by (1/3)).
The fourth term is 3 (which is obtained by multiplying the third term by (1/3)).
The fifth term is 1 (which is obtained by multiplying the fourth term by (1/3)).
Step-by-step explanation:
The given data represents a geometric sequence since there is a common ratio between each term. Let’s find the common ratio: The first term is 81. The second term is 27 (which is obtained by multiplying the previous term by (1/3)). The third term is 9 (which is obtained by multiplying the second term by (1/3)). The fourth term is 3 (which is obtained by multiplying the third term by (1/3)). The fifth term is 1 (which is obtained by multiplying the fourth term by (1/3)). The common ratio, denoted as (r), is (1/3). Now let’s write the exponential function that represents this sequence. We’ll use the general form of a geometric sequence: [ a_n = a_1 \cdot r^{(n-1)} ] where: (a_n) represents the (n)th term in the sequence. (a_1) represents the first term (which is 81 in this case). (r) represents the common ratio (which is (1/3)). Substituting the given values: [ a_n = 81 \cdot \left(\frac{1}{3}\right)^{(n-1)} ] Therefore, the correct exponential function that represents the given sequence is: B. (y = 81 \left(\frac{1}{3}\right)^x)
