[tex]\text{rate of increase i n number of tr}ees\text{ planted per day = }(1.087)^w\text{ (option B)}[/tex]Explanation:[tex]f(w)\text{ = }12(1.79)^w[/tex]
The function represents trees planted per number of weeks
where w = weeks
To get the function for the number of trees planted per day, we will find the relationship between weeks and days
7 days = 1 week
let 1 day = x
cross multiply:
7(x) = 1
x = 1/7
So, 1 day = 1/7 week =
since w = week
1 day = 1/7 w
We will substitute 1/7 w for w in the function:
[tex]\begin{gathered} f(w)=12(1.79)^{\frac{1}{7}w} \\ \\ \text{rate of increase of tr}ees\text{ planted per day = }(1.79)^{\frac{1}{7}w} \end{gathered}[/tex]
Expanding the parentheisis:
[tex]\begin{gathered} (1.79^{})^{\frac{1}{7}w}\text{ =}(1.79^{\frac{1}{7}})^w \\ 1.79^{\frac{1}{7}}\text{ = }1.0867 \\ 1.79^{\frac{1}{7}}\text{ = }1.087\text{ (3 decimal place)} \end{gathered}[/tex][tex]\text{(1.79)}^{\frac{1}{7}w}=(1.087)^w[/tex]
Hence, rate of increase in the number of trees per day is (1.087)^w (option B)
