The population of snails in a tank at the aquarium is found to triple every year. Mark visits the aquarium and counts 80 snails in the tank. Write a function, f(n), to model the number of snails in the tank n years after Mark's visit.
The snails are increasing exponentially. This requires an exponential growth model.
Such as y = ab^x, where {that is “y = a times b, to the x power”} a is the initial amount b is the growth factor x is the time period f(n) = 80(3)^n {that is “80 times 3, to the nth power”} 80 is the initial amount 3 indicates they are tripling each year n is the number of years after Mark’s visit For example: after the first year = 80(3)^1 = 240 after the second year = 80(3)² = 80(9) = 720 after the third year = 80(3)³ = 80(27) = 2160 As you can see, the number of snails is tripling each year. Here is another example involving exponential growth:
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February 2023
