Question

I need help with my hw i cant get it wrong

Answer 1

`\text{rate of increase i n number of tr}ees\text{ planted per day = }(1.087)^w\text{ (option B)}`Step-by-step explanation:
`f(w)\text{ = }12(1.79)^w`

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:

`\begin{gathered} f(w)=12(1.79)^{(1)/(7)w} \\ \\ \text{rate of increase of tr}ees\text{ planted per day = }(1.79)^{(1)/(7)w} \end{gathered}`

Expanding the parentheisis:

`\begin{gathered} (1.79^{})^{(1)/(7)w}\text{ =}(1.79^{(1)/(7)})^w \\ 1.79^{(1)/(7)}\text{ = }1.0867 \\ 1.79^{(1)/(7)}\text{ = }1.087\text{ (3 decimal place)} \end{gathered}`
`\text{(1.79)}^{(1)/(7)w}=(1.087)^w`

Hence, rate of increase in the number of trees per day is (1.087)^w (option B)