Answer: A. The expression [tex](1.05)^{6t}[/tex] reveals the approximate rate of increase in the number of subscribers if measured six times a year.
Step-by-step explanation:
Here, The number of subscribers to an online magazine is increasing by 34% each year. The function represents the number of subscribers after t years.
[tex]f(t) = 13,000(1.34)^t[/tex]
where [tex](1.34)^t[/tex] represents rate of increase in the number of subscriber.
If rate is measured six times a year
then the number of subscriber, [tex]f(6t)= 13000(1+0.34/6)^{6t}[/tex]
[tex]f(6t) = 13000( 1+0.05)^{6t}= 13000(1.05)^{6t}[/tex] ( approx)
Thus, when we measure increment in six times a year then the rate rate of increase in the number of subscribers=[tex](1.05)^{6t}[/tex]
Therefore Option A is correct.
Note: Option B) is incorrect because rate of increase in the number of subscribers if measured three times a year = [tex]13000(1.11)^{3t}[/tex] ( approx)
Option C) is incorrect because rate of increase in the number of subscribers if measured four times a year = [tex]13000(1.085)^{4t}[/tex] ( approx)
Option D) is incorrect because rate of increase in the number of subscribers if measured two times a year = [tex]13000(1.17)^{2t}[/tex] ( approx)
