Question

The population of a bacteria after x number of hours is modeled by the expression 1 , 000 ( 0 . 75 ) x . What is the rate of decay of the population of bacteria? A. 25% B. 75% C. 0.75% D. 1.25%

Answer 1

A 25%

Step-by-step explanation

the first thing we want to do for this problem is look at the exponential decay formula. its y=a(1-b)^x. "y" represents the final amount, "a" represents the original amount, and "b" represents the decay factor.

in this situation, .75 is the decay factor and our original amount is 1000. so to find out the decay factor, we need to subtract .75 from 1. you would get .25. .25 in percentage form is 25%.

we can double check by putting .25 in the orginal exponential decay formula. y=1000(1-.25)^x. 1-.25 equals .75, so now the equation is the same as our original equation, y=1000(0.75)^x

Answer 2

A. 25%

Explanation:

If you multiply something by 0.75, you're multiplying it by 75%, and that means you're losing 25% each time, so the rate of decay is 25%