Question

The growth of bacteria in a dish is modeled by the function f(t)=2 to the power of t/3. For which value of t is f(t)=32?

Answer 1

`\boxed{t=15}`

Explanation:

Function:
`f(t)=2^(t/3)`

You need to replace f(t) for 32 and isolate "t", like this:

`f(t)=2^(t/3)\\ 32=2^(t/3)\\ 2^5=2^(t/3)`

Since both bases are 2, we only take the powers:

`5=(t)/(3)\;\Longrightarrow 5\cdot3=t=15`