Question

a laboratory is studying the growth of a bacterial culture. the number of bacteria b(t) in the culture after t hours can be modeled by the expon equation $b(t)=100(2)^t$ calculate $b(-2)$.

Explanation:

Step1: Substitute t = -2 into the function

We have the function \( B(t) = 100(2)^{t} \). Substitute \( t=-2 \) into it, so we get \( B(-2)=100\times(2)^{-2} \).

Step2: Simplify the exponent

Recall the rule \( a^{-n}=\frac{1}{a^{n}} \), so \( 2^{-2}=\frac{1}{2^{2}}=\frac{1}{4} \). Then the expression becomes \( B(-2)=100\times\frac{1}{4} \).

Step3: Calculate the result

\( 100\times\frac{1}{4} = \frac{100}{4}=25 \).

Answer:

25