Cara tracked the population of fish in a pond. At the end of the first year, she counted 8 fish. Over the years, the population tripled each year.
Which equation can be used to determine the number of fish, f, after t years?
f = 3 ⋅ 8^(t-1)
f = 8 ⋅ 3^t
f = 3 ⋅ 8^t
f = 8 ⋅ 3^(t-1)
i think it may be f = 8 ⋅ 3^t ? not sure
or maybe it's f = 3 ⋅ 8^t ??
triples every year, so you multiply by powers of 3, not 8.
And since t=0 is the first year, after t years, it is 8*3^t
so pick B
says it's wrong
rubbish. For t=0, no years have passed, and you have the starting population of 8 fish.
After 1 year has passed, the population has tripled once, to 8*3 = 8*3^1
Note that the nth term of the GP is 8*3^(t-1) but that does not apply here.
To determine the equation that represents the number of fish, f, after t years, we need to analyze the given information.
We know that at the end of the first year, there were 8 fish. We are also told that the population triples each year. This means that for each year that passes, the number of fish is multiplied by 3.
Therefore, to determine the number of fish after t years, we need to start with the initial population of 8 fish and multiply it by 3^t (3 raised to the power of t) since the population triples each year.
So, the correct equation that represents the number of fish, f, after t years is:
f = 8 * 3^t
Hence, your choice of f = 8 * 3^t is correct.