Question

Can you please help me with this? No wrong answers plsss

Answer 1

f(1) = 203

f(2) = 206

f(3) = 209

Explanation:

Value of f(1)

To find the value of f(1), substitute n = 1 into the given function:

`\sf f(1)=f(1-1)+0.02f(1-1)\left(1-(f(1-1))/(800)\right)`

`\sf f(1)=f(0)+0.02f(0)\left(1-(f(0))/(800)\right)`

Now substitute f(0) = 200:

`\sf f(1)=200+0.02\cdot 200\left(1-(200)/(800)\right)`

`\sf f(1)=200+0.02\cdot 200\left(1-0.25\right)`

`\sf f(1)=200+0.02\cdot 200\left(0.75\right)`

`\sf f(1)=200+4\left(0.75\right)`

`\sf f(1)=200+3`

`\sf f(1)=203`

`\hrulefill`

Value of f(2)

To find the value of f(2), substitute n = 2 into the given function:

`\sf f(2)=f(2-1)+0.02f(2-1)\left(1-(f(2-1))/(800)\right)`

`\sf f(2)=f(1)+0.02f(1)\left(1-(f(1))/(800)\right)`

Now substitute f(1) = 203:

`\sf f(2)=203+0.02\cdot 203\left(1-(203)/(800)\right)`

`\sf f(2)=203+0.02\cdot 203\left(0.74625\right)`

`\sf f(2)=203+4.06\left(0.74625\right)`

`\sf f(2)=203+3.029775`

`\sf f(2)=206.029775`

`\sf f(2)=206 \;(nearest\;whole\;number)`

`\hrulefill`

Value of f(3)

To find the value of f(3), substitute n = 3 into the given function:

`\sf f(3)=f(3-1)+0.02f(3-1)\left(1-(f(3-1))/(800)\right)`

`\sf f(3)=f(2)+0.02f(2)\left(1-(f(2))/(800)\right)`

Now substitute f(2) = 206.029775:

`\sf f(3)=206.029775+0.02\cdot 206.029775\left(1-(206.029775)/(800)\right)`

`\sf f(3)=206.029775+0.02\cdot 206.029775\left(0.74246278125}\right)`

`\sf f(3)=206.029775+4.1205955\left(0.74246278125}\right)`

`\sf f(3)=206.029775+3.05938879533...`

`\sf f(3)=209.08916379...`

`\sf f(3)=209 \;(nearest\;whole\;number)`