Question

A video game begins with five characters. Doing the game, each character splits and becomes 2 new characters every hour. The character population is shown in the graph below​

Answer 1

12. The growth factor is 2. This refers to the characters doubling every hour. The equation that models this is y = 5*2^x. It is in the form y = a*b^x with a = 5 as the starting value and b = 2 as the growth factor.

13. The y intercept is 5. Visually this is where the graph crosses the y axis. It is located at the point (0,5). This is connected directly to the value of 'a' in the equation mentioned in problem 12.

14. The y intercept represents the starting amount of characters (5). The y intercept always occurs when x = 0 to indicate the starting amount. Put another way, when x = 0 hours, there are y = 5 characters to start from.

Answer 2

Answer:  12) 2

               13) 5

               14)  the y-int is the # of characters the game starts with

Step-by-step explanation:

NOTE: This is the graph of an exponential function which is of the form:

            y = a(b)ˣ    where

• "a" is the initial value (starting point)
• "b" is the growth factor (rate of increase or decrease)

12) Notice that each y-value is double the previous value.  This means the growth factor is 2

13) The y-intercept is where the graph crosses the y-axis.  In the given graph, it crosses the y-axis at the midpoint between 0 and 10, which is 5.

14) The y-intercept is the initial value (starting point), which is the number of characters at the beginning of the game.

Bonus: The equation of the graph is: y = 5(2)ˣ