Question

An invasive vine was spotted growing in a nearby forest. It was 18 feet long when first observed, but it's been growing by 45.5% each day.

Define a function f to represent the vine's length (in feet) n days since it was first observed.

Answer 1

The function representing the length of the invasive vine after n days is
`f(n) = 18 x (1 + 0.455)^n`, where 18 is the original length, 0.455 is the daily growth rate, and n is the number of days since observation.

Step-by-step explanation:

To represent the growth of an invasive vine in a function, we can define f(n) as the length of the vine n days since it was first observed. Since the vine's initial length is 18 feet and it grows at a rate of 45.5% daily, the function f(n) would be:

`f(n) = 18 x (1 + 0.455)^n`

Here, 18 is the original length of the vine in feet, 0.455 represents the 45.5% daily growth rate, and n is the number of days since the vine was first spotted. The exponential function indicates the rapid and continuous growth of the invasive species, a prime illustration of how non-native plants like kudzu can become problematic, as seen in the southeastern United States where kudzu has overpowered local vegetation.