Question

At the beginning of an environmental study a forest cover an area of 1500 km second power since then this area has decreased by 9.8% each year let T be the number of years since the start of the study letter y b the area that the forest covers in km to the second power write an exponential function showing the relationship between Y&T

Answer 1

Answer:

$y=1500\cdot(0.902)^T$

Step-by-step explanation:

Let T be the number of years since the start of the study and y be the area that the forest covers in $\text{km}^2$.

We have been given that at the beginning of an environmental study a forest cover an area of 1500 $\text{km}^2$. Since then this area has decreased by 9.8% each year.

We know that an exponential function is in form $y=a\cdot(1-r)^x$, where,

y = Final amount,

a = Initial amount,

r = Decay rate in decimal form,

x = Time.

Let us convert 9.8% into decimal as:

$9.8\%=\frac{9.8}{100}=0.098$

We have been given that initial value (a) is $1500$.

Upon substituting our given values, we will get:

$y=1500\cdot(1-0.098)^T$

$y=1500\cdot(0.902)^T$

Therefore, our required exponential function would be $y=1500\cdot(0.902)^T$.