Question

the function $f(t)=40000(2)^{\frac{t}{790}}$ gives the number of bacteria in a population $t$ minutes after an initial observation. how much time, in minutes, does it take for the number of bacteria in the population to double? a) 2 b) 790 c) 1580 d) 40000

Explanation:

Step1: Let the initial number of bacteria be $f(0)$.

$f(0)=40000(2)^{\frac{0}{790}} = 40000$

Step2: Let the time when the population doubles be $t$. Then $f(t)=2\times40000 = 80000$.

Set up the equation $80000=40000(2)^{\frac{t}{790}}$.

Step3: Simplify the equation.

Divide both sides of the equation by 40000: $\frac{80000}{40000}=(2)^{\frac{t}{790}}$, so $2=(2)^{\frac{t}{790}}$.

Step4: Solve for $t$.

Since the bases are the same, the exponents must be equal. So $\frac{t}{790}=1$, and $t = 790$.

Answer:

B. 790