Question

type the correct answer in the box. use numerals instead of words. the average number of subscribers to an online magazine each year from 2010 to 2015 is given in the table below. number of years since 2010 avg. number of subscribers 0 320,000 1 384,000 2 460,800 3 552,960 4 663,552 5 769,262 the percent increase in the average number of subscribers each year since 2010 was %

Explanation:

Step1: Recall percent - increase formula

Percent increase=$\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times100$

Step2: Take the first two data - points

Let the old value (at year 0) be $a = 320000$ and the new value (at year 1) be $b = 384000$.

Step3: Calculate the percent increase

Percent increase=$\frac{384000 - 320000}{320000}\times100=\frac{64000}{320000}\times100 = 20\%$
We can check with other consecutive data - points. Let's take the second and third data - points. Old value $a = 384000$ and new value $b = 460800$.
Percent increase=$\frac{460800 - 384000}{384000}\times100=\frac{76800}{384000}\times100 = 20\%$
We can continue this for all consecutive pairs of data - points. Since the ratio of the increase to the previous value is the same for all consecutive years, the percent increase in the average number of subscribers each year since 2010 is 20%. So the number of subscribers is increasing by a factor of $1 + 0.2=1.2$ each year. If we consider the general growth formula $y = a(1 + r)^x$, where $y$ is the number of subscribers, $a$ is the initial number of subscribers, $r$ is the rate of growth, and $x$ is the number of years since 2010. Here $r = 0.2$ or 20% and the factor by which the number of subscribers is multiplied each year is $1 + r=1.2$ or 120% (when expressed as a percentage of the previous - year's value). So the answer is 120.

Answer:

120