To begin a bacteria study, a petri dish had 2800 bacteria cells. Each hour since, the number of cells has increased by 7.2%. 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.
Question
The function that models exponential growth is:
P(t) = P0*(1 + r)^t, where
P0 = P(0) is the initial value of P
r is the growth rate as a decimal
In our case we have:
P(0) = 2800
r = 0.035 or 3.5%
P(t) = 2800*(1 + 0.035)^t
P(t) = 2800*(1.035)^t
The same exponential function written using y and t is:
y = 2800*1.035^t.
Explanation: https://softmath.com/algebra-word-problems/to-begin-a-bacteria-study-a-petri-dish-had-2800-bacteria