Question

20
the function (f(t)=60000(2)^{\frac{t}{110}}) 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?
21
the function (f) is defined by (f(x)=a^{x}+b), where (a) and (b) are constants and (a > 0). in the (xy - plane), the

Explanation:

Step1: Set up the equation

Let the initial number of bacteria be $f(0)=60000(2)^{\frac{0}{110}} = 60000$. We want to find $t$ when the number of bacteria doubles, so $f(t)=2\times60000$. Then the equation is $60000(2)^{\frac{t}{110}}=2\times60000$.

Step2: Simplify the equation

Divide both sides of the equation by 60000, we get $(2)^{\frac{t}{110}} = 2$.

Step3: Solve for $t$

Since the bases are the same ($a^m=a^n$ implies $m = n$ for $a>0,a
eq1$), and here $a = 2$, we have $\frac{t}{110}=1$. Multiply both sides by 110, so $t = 110$.

Answer:

110