Question

Farmers are fighting a fungal growth that can cause crop failure. If 1,959 hectares of farmland are infected right now, and the infected area decreases by 10% every year, how much farmland will be infected in 10 years?If necessary, round your answer to the nearest tenth.

Answer 1

`683.1ha`

1) Let's model an equation for that fungal growth. Notice that the infected area is decreasing by 10% yearly, so we can write the factor for this exponential model this way:

`\begin{gathered} (1-0.1) \\ (0.9) \end{gathered}`

2) Notice that besides this, we were told that the period to be considered is 10 years so we can write out the following, bearing in mind the initial area as well:

`\begin{gathered} A=1959(0.9)^t \\ A=1959(0.9)^(10) \\ A\approx683.1 \end{gathered}`

So, as we can see by the rate of infection, this fungal growth has been declining. And in ten years the infected area will be 683.1 ha