Question

the equation $y = 26(1.065)^x$ represents the number of people that are signed up for a tournament after x days. which statement best describes the number of people that are signed up for the tournament? the number of people signing up for the tournament is increasing by 6.5% each day. the number of people signing up for the tournament is decreasing by 6.5% each day. the number of people signing up for the tournament is increasing by 26 people each day. the number of people signing up for the tournament is increasing by 0.65% each day. question 10

Explanation:

Step1: Recall exponential - growth formula

The general form of an exponential - growth formula is $y = a(1 + r)^x$, where $a$ is the initial amount, $r$ is the growth rate as a decimal, and $x$ is the number of time - periods.

Step2: Identify values in given equation

In the equation $y = 26(1.065)^x$, we can rewrite $1.065$ as $1+0.065$. Here, $a = 26$ and $r=0.065$.

Step3: Convert growth rate to percentage

To convert the growth rate $r = 0.065$ to a percentage, we multiply by 100. So, $0.065\times100 = 6.5\%$. This means the quantity $y$ (the number of people signed up) is increasing by $6.5\%$ each day.

Answer:

The number of people signing up for the tournament is increasing by 6.5% each day.