Question

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n = f(t) = 100·2ᵗ/³.

Find the inverse of this function.
f⁻¹(n) = ____

Answer 1

The inverse of the function f(t) = 100 * 2^(t/3) is f^(-1)(n) = (3/log(2)) * log(n/100).

Step-by-step explanation:

To find the inverse of a function, we need to switch the roles of the dependent and independent variables. In this case, the function is given as f(t) = 100 * 2^(t/3). Let's call the inverse function f^(-1)(n). We can rewrite the original function as t = (3/log(2)) * log(n/100). Therefore, the inverse function is f^(-1)(n) = (3/log(2)) * log(n/100).