Please show work Thanks Use exponential regression to find a

Use exponential regression to find a function that models this data When will the number of bacteria reach 2500? How many bacteria will exist after 1 hour?

Solution

The formula for bacterial growth is A = Pe^kt where, p is the initial quantity of bacteria, k is a constant and A is the quantity of bacteria after t minutes. Here, when t = 1, we have P = 413. Therefore 413 = Pe^k …(1) Also, when t = 3, A = 575. Therefore, 575 = Pe^3k …(2) On dividing 2^nd equation by the 1^st equation, we get Pe^3k/ Pe^k = 575/413 or, e^2k = 1.392251816 . Also e^k = 575/413 = 1.179937209 . On taking natural logarithms of both the sides, we have k lne = ln 1.179937209 or k = 0.165461224 = 0.1655 ( on rounding off to 4 decimal places) ( as ln e = 1). From the 1^st equation, we have P = 313/e^k =    413/ 1.179937209 = 350.0186254 or, 350 (on rounding off to the nearest whole number. Theerefore, the required function is A = 350e^0.1655t We can verify the result by substituting other values of t in this equation.