Question

A small island has a roughly rectangular shape. It is 18.2 kilometers wide and 28.5 kilometers long. Rising water levels are reducing the width by 1.2% each year and the length by 0.8% each year.

Use the drop-down menus to choose or create functions to model:

A. The width of the island over time, w(t)
B. The length of the island over time, l(t)
C. The area of the island over time, a(t)

Answer 1

Answer:

Part A) $W(t)=18.2(1.012)^t$

Part B) $L(t)=28.5(1.008)^t$

Part C) $A(t)=518.7(1.020096)^t$

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

$y=a(1+r)^x$

where

a is the initial value

r is the rate of change

Part A) Create functions to model :

The width of the island over time, w(t)

we have

$W(t)=a(1+r)^t$

where

$a=18.2\ km\\r=1.2\%=1.2/100=0.012$

substitute

$W(t)=18.2(1+0.012)^t$

$W(t)=18.2(1.012)^t$

Part B) Create functions to model :

The length of the island over time, l(t)

we have

$L(t)=a(1+r)^t$

where

$a=28.5\ km\\r=0.8\%=0.8/100=0.008$

substitute

$L(t)=28.5(1+0.008)^t$

$L(t)=28.5(1.008)^t$

Part C) Create functions to model :

The area of the island over time, a(t)

we have

$W(t)=18.2(1.012)^t$

$L(t)=28.5(1.008)^t$

Remember that the area of a rectangle is given by

$A=LW$

substitute the given values

$A(t)=(28.5(1.008)^t)(18.2(1.012)^t)$

$A(t)=(28.5*18.2)(1.008*1.012)^t)$

$A(t)=518.7(1.020096)^t$

Answer 2

Answer:

Here's the answer ;)