Question

I need help number 10

Answer 1

a)

• Initial population: 40

,

• Rate of growth: 13%

Function

$f(x)=40\cdot1.13^x$

To know which graph represents the function, we have to replace a value, for example, x = 5.

$f(5)=40\cdot1.13^5=73.70$

As we can see based on the image given, the blue line is the one that approximates most to ( 5, 73 ).

b)

• Initial population: 40

,

• Rate of growth: 17%

$g(x)=40\cdot1.17^x$

Also, we will replace the value of x = 5.

$g(5)=40\cdot1.17^5=87.70$

As we can see based on the image given, the red line is the one that approximates most to ( 5, 87 ).

c)

As it is a linear function, this will have the form:

$y=mx+b$

In this case, b represents the initial population and m represents the rate of change. Therefore...

$h(x)=20x+40$

And this is represented by the green line (as it is linear).

Answers:

a)

$f(x)=40\cdot1.13^x$

f( x ) is represented by the blue line.

b)

$g(x)=40\cdot1.17^x$

g( x ) is represented by the red line.

c)

$h(x)=20x+40$

h( x ) is represented by the green line.