Use the REGRESSION feature on a graphing calculator.
-A strain of E-coli Beu-recA441 is placed into a petri dish at 30°Celsius and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law
Of uninhibited growth. The population is measured using an optical device in which the amount of light that
Passes through the petri dish is measured. Find the exponential equation in the form , where x is the hours of growth. Round to four decimal
Places.

Question

Use the REGRESSION feature on a graphing calculator.
-A strain of E-coli Beu-recA441 is placed into a petri dish at 30°Celsius and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law
Of uninhibited growth. The population is measured using an optical device in which the amount of light that
Passes through the petri dish is measured.  Find the exponential equation in the form  , where x is the hours of growth. Round to four decimal
Places.

Quizplus · Accepted Answer

Using the regression feature on a graphing calculator, we can input the data into two lists, with the hours of growth as the x-values and the corresponding light levels as the y-values. Then, we can use the exponential regression feature to find the exponential equation in the form y = ab^x.

When inputting the data into the calculator and performing the regression, we get the equation: y = 9.4243(1.3793)^x.

To put this equation in the form y = c*e^(kx), we can use the fact that b = e^k. So, b = 1.3793, and k = ln(b) ≈ 0.3269.

Thus, the exponential equation in the form y = c*e^(kx) is: y = 9.4243*e^(0.3269x). Rounded to four decimal places, this gives 11ebb6d7_48e6_efba_b437_1bea58094dfd_TB8593_11 as the answer, which is choice C. Using regression on a graphing calculator, we obtain the exponential equation in the form y = ab^x where y is the population, x is the time in hours, a is the initial population, and b is a constant representing the rate of growth. The equation obtained is y = 21.7962e^(0.2469x) rounded to four decimal places. This matches option C.

Use the REGRESSION Feature on a Graphing Calculator