Question

Scientists are studying a bacteria sample. The function f of x equals 256. 1.15 to the x. gives the number of bacteria in the sample at the end of x days. Which statement is the best interpretation of one of the values in this function?

Answer 1

the number of bacteria increases at a rate of 15% each day

Explanation:

Given the function :

f(x) = 256(1.15)^x

The function represents an exponential growth function ; comparing the equation with the general form of an exponential growth function :

f(x) = A(1 + r)^t

A = the initial value of the population, = 256

(1 + r),; r = growth rate

Therefore, to solve for r ;

1 + r = 1.15

r = 1.15 - 1 ; r = 0.15

Hence, growth rate = 0.15 = 0.15 * 100% = 15%

Hence, the number of bacteria increases at a rate of 15% each day