Bacteria is growing in a petri dish. Initially, there were 15,000 bacteria in the dish. It triples every 8 hours. Write the equation to represents this growth after t hours.
n(t) = 15000*3^(t/8)
To represent the growth of bacteria in a petri dish after t hours, we can use the exponential growth formula:
N(t) = N₀ * (r^t)
Where:
N(t) = the number of bacteria after t hours
N₀ = the initial number of bacteria (15,000 bacteria)
r = growth rate (in this case, 3 because it triples every 8 hours)
t = time in hours
Therefore, the equation that represents the growth of bacteria after t hours is:
N(t) = 15,000 * (3^(t/8))
To write the equation representing the growth of bacteria in the petri dish after t hours, we need to consider two things:
1. The initial number of bacteria: 15,000
2. The growth rate: the bacteria triples every 8 hours.
Since the bacteria triples every 8 hours, we can express the growth rate as a factor of 3. To determine how many times the bacteria tripled within t hours, we divide t by 8. This gives us (t/8) as the number of tripled growth cycles.
Now, let's write the equation for the growth of bacteria after t hours:
Number of bacteria = Initial number of bacteria * Growth rate^Number of growth cycles
Substituting the known values into the equation:
Number of bacteria = 15,000 * (3)^(t/8)
Therefore, the equation representing the growth of bacteria after t hours is:
Number of bacteria = 15,000 * (3)^(t/8)