The rate of bacteria growth in a laboratory experiment was measured at 14% per hour. If this experiment is repeated and begins with 7 grams of bacteria, how much bacteria should be expected after 15 hours? Round to the nearest tenth of a gram.
Bacteria = 7 + 0.14*7*15 =
the growth is exponential ... new bacteria give rise to more, and so on
7 g * (1 + 0.14)^15
To calculate the amount of bacteria expected after 15 hours, we'll use the formula for exponential growth:
A = P (1 + r/n)^(nt)
Where:
A is the amount of bacteria after time t
P is the initial amount of bacteria
r is the growth rate (expressed as a decimal)
n is the number of times the growth rate is compounded per time period
t is the time period
In this case:
P = 7 grams
r = 14% per hour, which is 0.14 (expressed as a decimal)
n = 1 (since the growth rate is measured per hour)
t = 15 hours
Substituting these values into the formula:
A = 7 * (1 + 0.14/1)^(1*15)
A = 7 * (1 + 0.14)^15
A ≈ 7 * (1.14)^15
A ≈ 7 * 4.91157
Now, we can calculate the approximate value of A:
A ≈ 34.381 grams
Rounding to the nearest tenth of a gram:
A ≈ 34.4 grams
Therefore, after 15 hours, we can expect approximately 34.4 grams of bacteria.