SOLUTION: Bacteria are growing in a culture, and their number is increasing at the rate of 5 % an hour . Initially , 400 bacteria are present. (a) Determine an equation that gives the n

Algebra ->  Finance -> SOLUTION: Bacteria are growing in a culture, and their number is increasing at the rate of 5 % an hour . Initially , 400 bacteria are present. (a) Determine an equation that gives the n      Log On


   

Question 1126437: Bacteria are growing in a culture, and their number is increasing at the rate of 5 % an hour . Initially , 400 bacteria are present.

(a) Determine an equation that gives the numbet, N of bacteria present after t hours.
(b) How many bacteria are present after one hour and After four hour
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula to use with this is f = p * (1 + r) ^ t

f is the future value
p is the present value
r is the interest rate per time period
t is the number of time periods.

you are given that the number of the bacteria is increasing at the rate of 5% per hour.

your time period is therefore in hours, so t represents the number of hours.
your rate of growth per hour is equal to 5% / 100 = .05, so r = .05.

the formula becomes f = p * (1 + .05) ^ t

since 400 bacteria are initially present, then p = 400.

the formula becomes f = 400 * (1 + .05) ^ t

after one hour, t = 1 and the formula becomes f = 400 * (1 +.05) ^ 1 = 400 * 1.05 = 420.

after 4 hours, t = 4 and the formula becomes f = 400 * (1 + .05) ^ 4 = 400 * 1.05^4 = 486.2025.

let y = f and x = t and you can graph this equation as shown below.

$$$