A bacterial culture in a petri dish grows at an exponential rate. The petri dish has an area of 256 mm2, and the bacterial culture stops growing when it covers this area. The area in mm2 that the bacteria cover each day is given by the function ƒ(x) = 2x. What is a reasonable domain for this function?

Answer:x  ∈ [0,8]Step-by-step explanation:We need to find the value of x such that2^x = 256We know that256 = 2^8Therefore2^x = 2^8Since both sides of the equation have the same base, it must mean thatx = 8So, ƒ(8) = 2^(8) = 256 mm^2The domain of the function isx  ∈ [0,8]