Question

I am very confused on what to do.Can someone help me?

Answer 1

739 m²

Explanation:

`\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Equation}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}`

The given scenario can be modelled as an exponential equation.

Let y be the area the fire covers (in meters squared).

Let x by the time (in hours).

If the fire currently covers an area of 32 m² then the initial value, a, is 32.

If the area covered by the fire increases by 17% each hour, then the growth factor, b, is 1.17 (since an increase of 17% is 117% of the previous amount).

Therefore:

• a = 32
• b = 1.17

Substitute the values of a and b into the exponential formula:

`y=32(1.17)^x`

To find the area that the first covers in 20 hours' time, simply substitute x=20 into the equation:

`\implies y=32(1.17)^(20)`

`\implies y=32(23.1055991...)`

`\implies y=739.37917...`

Therefore, the area the fire will cover in 20 hours' time is 739 m² (nearest 1 m²).