Question

The accompanying table shows the number of bacteria present in a certain culture over a 4 hour period, where x is the time, in hours, and y is the number of bacteria.Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the number of bacteria present after 16 hours, to the nearest whole number.

Answer 1

Answer:

Step-by-step explanation:

I really hope you know how to use your calculator to find regression equations, because in this forum it is impossible to teach you how to do that. I ran the data through my calculator and got the exponential equation as

$y=1963.56(1.14)^x$ which means at 4 hours, we started with 1963 bacteria and it is growing at a rate of 114% each hour. Since we started out with an x value of 0, and that value represents the number of bacteria after 4 hours, then time 0 is 4 hours, which means that time 12 is 16 hours. We replace the x in the equation with a 12 and do the math:

$y=1963.56(1.14)^{12$ which gives us, in the end,

y = 9460