Exercise 5 Page 484

y= a b^x, where b>0 Here y represents the dependent variable, a stands for the initial amount, b is the growth factor, and x is the independent variable. At the beginning of the experiment, the time is 0 hours and there are 6000 bacteria cells. When x=2, the number of bacteria cells is 28 000. We can use this information to assign values to the variables. a= 6000 x= 2 y= 28 000 We are left unknown with the variable b, which we will solve for by substituting all our known values into the function. y= a b^x ⇔ 28 000= 6000 b^2 We will now take our function and simplify it to solve for our growth factor, b.

By simplifying our equation, we find that b≈ 2.16025. We will substitute this value, along with our value of a, to find a function that models the number of bacteria after x hours. y= a b^x ⇔ y= 6000( 2.16025)^x The function that models the number of bacteria after x hours is y=6000(2.16025)^x.