The population of an endangered species was estimated to be 240 in 2018. The population has been tracked each year and has been modeled with the geometric sequence 240, 360, 540, 810, . . . . Create a function that models this situation.(1 point)

Question

Responses

f(n)=240(3/2)n−1
f left parenthesis n right parenthesis equals 240 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript n minus 1 baseline

f(n)=240(1/2)n−1
f left parenthesis n right parenthesis equals 240 left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis superscript n minus 1 baseline

f(n)=240+(n−1)1/2
f left parenthesis n right parenthesis equals 240 plus left parenthesis n minus 1 right parenthesis Start Fraction 1 over 2 End Fraction

f(n)=240(120)n−1

Answer 1

To model the population of the endangered species using a geometric sequence, we need to determine the first term and the common ratio.

Given the sequence: 240, 360, 540, 810, ...

1. The first term \( a_1 = 240 \).
2. The second term is \( a_2 = 360 \).
3. To find the common ratio \( r \), we can divide the second term by the first term: \[ r = \frac{a_2}{a_1} = \frac{360}{240} = 1.5 = \frac{3}{2} \]

Thus, the common ratio is \( \frac{3}{2} \).

The general form of a geometric sequence can be written as: \[ f(n) = a_1 \cdot r^{n-1} \] Substituting in the values we found: \[ f(n) = 240 \left(\frac{3}{2}\right)^{n-1} \]

Therefore, the correct function that models this situation is: \[ \boxed{f(n) = 240 \left(\frac{3}{2}\right)^{n-1}} \]