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

Answer:

$\boxed{t=15}$

Step-by-step 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:

$5=\dfrac{t}{3}\;\Longrightarrow 5\cdot3=t=15$