College

The inches of rainfall on Mount Waialeale on Kauai in Hawaii are represented by the function [tex]f(x) = 3^x + 1 - 22[/tex]. Scientists are using equations to study rainfall from year to year.

Calculate how much rainfall there was in year four and in year nine. Show all of your work and calculations.

Answer :

Answer:

[tex] \textrm {221 in year 4} \\ \textrm{59027 in year 9}[/tex]

Step-by-step explanation:

we are given a function

[tex] \displaystyle f(x) = {3}^{x + 1} - 22[/tex]

where x represents the years f(x) represents the amount of rainfall

so to figure out the amount of rainfall in year 4 we can substitute 4 for x

[tex] \displaystyle f(4) = {3}^{4+ 1} - 22[/tex]

simplify addition:

[tex] \displaystyle f(4) = {3}^{5} - 22[/tex]

simplify square:

[tex] \displaystyle f(4) = 243- 22[/tex]

simplify substraction:

[tex] \displaystyle f(4) = 221[/tex]

likewise In the year 9

[tex] \displaystyle f(9) = {3}^{9 + 1} - 22[/tex]

simplify addition:

[tex] \displaystyle f(9) = {3}^{10} - 22[/tex]

simplify square:

[tex] \displaystyle f(9) = 59049 - 22[/tex]

simplify Substraction:

[tex] \displaystyle f(9) = 59027[/tex]

hence,

there was 221 and 59027 in year four and In year nine
F(x)=3^x+1-22 is the question

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