To begin a bacteria study, a petri dish had 1500 bacteria cells. Each hour since, the number of cells has increased by 7.1%.
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.
y = 1500 (1.071)^t , where t is in hours
To start, let's analyze the given information. We know that at the beginning of the study, there were 1500 bacteria cells. Then, every hour, the number of cells increased by 7.1%.
The term "exponential function" indicates that the relationship between y (the number of bacteria cells) and t (the number of hours) follows an exponential pattern. In this case, since the number of cells increases by a constant percentage, we can express it using an exponential growth function.
The general form of an exponential growth function is: y = a(1 + r)^t, where "a" is the initial value, "r" is the growth rate as a decimal, and "t" represents time.
In this scenario, the initial value "a" is given as 1500, so our equation becomes: y = 1500(1 + r)^t.
To determine the value of "r," we know that the number of cells increases by 7.1% each hour. As a decimal, this growth rate is 0.071 (since 7.1% = 7.1/100 = 0.071). Therefore, we substitute "r" with 0.071 in the equation: y = 1500(1 + 0.071)^t.
Simplifying further, the exponential function representing this relationship between y (the number of bacteria cells) and t (the number of hours) is:
y = 1500(1.071)^t.