Question

if a bacteria population starts with 100 bacteria and doubles every two hours, then the number of bacteria after t hours is n = f(t) = 100 · 2t⁄2.(a)find the inverse of this function.

Answer 1

To find the inverse of the function n = f(t) = 100 · 2t/2, replace n with x, swap x and t, and solve for t.

Step-by-step explanation:

The given function is n = f(t) = 100 · 2t/2.

To find the inverse of this function, we need to solve for t.

1. Replace n with x.
2. Swap x and t.
3. Solve the equation for t.

Starting with the given function:

x = 100 · 2t/2

Swapping x and t, we have:

t = 100 · 2x/2

Simplifying, we get:

t = 100 · 2x/2

Therefore, the inverse of the function is f-1(x) = t = 100 · 2x/2.