Problema Solution
To begin a bacteria study a petri dish had 2600 bacteria cells. Each hour since, the number of cells has increased by 7.4%
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells
Write an exponential function showing the relationship between y and t.
Answer provided by our tutors
at the start:
t = 0
y = 2600
after 1 hour:
t = 1 hr
y = 2600 + 0.074*2600
y = 2600(1 + 0.074)
after 2 hours:
t = 2 hr
y = 2600(1 + 0.074) + 2600(1 + 0.074)*0.074
y = 2600(1 + 0.074)^2
after 3 hours
t = 3 hr
y = 2600(1 + 0.074)^3
thus the exponential function is:
y = 2600(1 + 0.074)^t
we can also prove the above equation using the method of Mathematical induction.