Scientists have developed a model to predict the growth of bacteria in bologna sausage at 32°C. The number of bacteria is given by

where N₀ is the number of bacteria present at the beginning of the experiment and N(t) is the number of bacteria present at time t (in hours).

(a) Use the properties of logarithms to find an expression for N(t). Assume that N₀ = 1000.
(b) Use a graphing calculator to estimate the derivative of N(t) when t = 20 and interpret.
(c) Let S(t) = ln(N(t)/N0). Graph S(t) on [0, 35] by [0, 12].
(d) Graph N(t) on [0, 35] by [0, 20,000,000] and compare the graphs from parts (c) and (d).

(e) Find lim_t→∞S(t) and then use this limit to find lim_t→∞ N(t).

In (N(7) = 9.8901e e2.54197-0.21671