Question

5 multiple choice 1 point which explicit formula can be used to determine the number of triangles in figure n? figure 1 figure 2 figure 3 a_n = 2(4)^{n - 1} a_n = 4 + 2n a_n = 4n a_n = 4(2)^{n - 1} 6 multiple choice 1 point the population of a bacterial colony, p, is modeled by the function p(h) = 500(2)^h, where h is the number of hours since the observation began. what is the appropriate domain for this function? h ≥ 0 h must be an integer (no decimals

Explanation:

Step1: Analyze the number of triangles in each figure

Figure 1 has \(4\) triangles (\(n = 1\), \(a_{1}=4\)), Figure 2 has \(8\) triangles (\(n = 2\), \(a_{2}=8\)), Figure 3 has \(16\) triangles (\(n = 3\), \(a_{3}=16\)). This is a geometric sequence with first - term \(a_{1}=4\) and common ratio \(r = 2\).

Step2: Use the formula for the \(n\)th term of a geometric sequence

The formula for the \(n\)th term of a geometric sequence is \(a_{n}=a_{1}r^{n - 1}\). Substituting \(a_{1}=4\) and \(r = 2\) into the formula, we get \(a_{n}=4\times(2)^{n - 1}\).

Answer:

\(a_{n}=4(2)^{n - 1}\)