Question

if a bacteria population starts with 80 bacteria and doubles every four hours, then the number of bacteria after t hours is n = f(t) = 80 · 2t⁄4. (a) find the inverse of this function.

Answer 1

To find the inverse of a function, we solve for the variable in terms of the given value. We can find the inverse of the function n = 80 · 2^(t/4) by dividing both sides by 80 and taking the logarithm of both sides. Finally, multiplying by 4 gives us t in terms of n.

Step-by-step explanation:

To find the inverse of the function f(t) = 80 · 2t⁄4, we need to solve for t in terms of n.

Starting with the original function, n = 80 · 2t⁄4, we can isolate t by dividing both sides of the equation by 80.

So, n/80 = 2t⁄4.

To get rid of the exponent, we can take the logarithm of both sides. Using the logarithm base 2, we have log2(n/80) = t⁄4.

Finally, multiplying both sides by 4 gives us t = 4 log2(n/80).