1717 bacteria will be present after 17 hours
Solution:
The exponential growth function is given as:
[tex]y = a(1+r)^t[/tex] --------- eqn 1
Where,
y is future value
a is initial value
r is growth rate in decimal
t is time period
A culture started with 1,000 bacteria. After 3 hours, it grew to 1,100 bacteria
Therefore,
Substitute a = 1000, y = 11000 and t = 3 in eqn 1
[tex]1100 = 1000(1 + r)^3\\\\(1+r)^3 = \frac{1100}{1000}\\\\(1+r)^3 = 1.1\\\\Take\ cube\ root\ on\ both\ sides\\\\1 + r = \sqrt[3]{1.1} \\\\1 + r = 1.0323[/tex]
Predict how many bacteria will be present after 17 hours.
Substitute a = 1000 and t = 17 and 1 + r = 1.0323 in eqn 1
[tex]y = 1000(1.0323)^{17}\\\\y = 1000 \times 1.716725\\\\y = 1716.725 \approx 1717[/tex]
Thus 1717 bacteria will be present after 17 hours
