2
answers
0
watching
97
views
23 May 2018
[4] 7. (a) A function f is said to grow exponentially when f'(x) = kf() for some non-zero constant k and all x in R. If f grows exponentially, prove that the function g(t) = is a constant function. [1] (b) If (b) If f grows exponentially, use part (a) to show that f(x) = Aek for some constant A. [5] (c) The population in a dish of bacteria is growing exponentially. At the start there are 8 micro- units of bacteria in the dish and the population doubles every 3 hours. How long will it take for the population to reach 20 micro-units?
[4] 7. (a) A function f is said to grow exponentially when f'(x) = kf() for some non-zero constant k and all x in R. If f grows exponentially, prove that the function g(t) = is a constant function. [1] (b) If (b) If f grows exponentially, use part (a) to show that f(x) = Aek for some constant A. [5] (c) The population in a dish of bacteria is growing exponentially. At the start there are 8 micro- units of bacteria in the dish and the population doubles every 3 hours. How long will it take for the population to reach 20 micro-units?
Nestor RutherfordLv2
25 May 2018
Already have an account? Log in
, as an exponential function of the time elapsed since the experiment began.
. Is that what was expected from our exponential growth model?
