Question

The number of subscribers to an online magazine is increasing by 34% each year. The function represents the number of subscribers after t years.
f(t) = 13,000(1.34)^t



Which statement is true?

A.
The expression (1.05)6t reveals the approximate rate of increase in the number of subscribers if measured six times a year.
B.
The expression (1.15)3t reveals the approximate rate of increase in the number of subscribers if measured three times a year.
C.
The expression (1.03)4t reveals the approximate rate of increase in the number of subscribers if measured four times a year.
D.
The expression (1.12)2t reveals the approximate rate of increase in the number of subscribers if measured two times a year.

Answer 1

Answer: A.  The expression  $(1.05)^{6t}$ 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.

$f(t) = 13,000(1.34)^t$

where $(1.34)^t$ represents rate of increase in the number of subscriber.

If rate is measured six times a year

then the number of subscriber, $f(6t)= 13000(1+0.34/6)^{6t}$

$f(6t) = 13000( 1+0.05)^{6t}= 13000(1.05)^{6t}$ ( approx)

Thus, when we measure increment in six times a year then the rate  rate of increase in the number of subscribers=$(1.05)^{6t}$

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 = $13000(1.11)^{3t}$ ( approx)

Option C) is incorrect because rate of increase in the number of subscribers if measured four times a year =  $13000(1.085)^{4t}$ ( approx)

Option D) is incorrect because rate of increase in the number of subscribers if measured two times a year =  $13000(1.17)^{2t}$ ( approx)