Question

The number of bacteria can be represented by the equation A(t)=200(.75)^t, wherr A(t) is the amount of bacteria in grams and t is the number of days. a. Is this function growth or decay? b. What percent is the bacteria decreasing by each day? c. How many grams of bacteria will there be in 1 week? d. After how many days will there be half the initial amount of bacteria left?

Answer 1

Explanation:

a. This is a decay function, since the final value (A) gets smaller and smaller as the days pass by.

b. The bacteria is decreasing by 75% per day exponentially.

c. In order to calculate the amount of bacteria in a week we simply substitute the variable t for 7 (7 days in a week) and solve for A

A = 200(0.75)^7

A = 26.7 bacteria after 1 week

d. In order to calculate this we need to substitute the variable A with 100 and solve for t

100 = 200(0.75)^t ... divide both side by 200

0.5 = 0.75^t

`(ln(0.5))/(ln(0.75))` = t

2.4 = t

It will be half the initial amount after 2.4 days.