exponential and logarithmic functions (1 Viewer)

[pLuvia]

The population P of a certain kind of insects is given by P(t)= a/b+e^-at, where a and b are positive constants.

(a) Find the initial population
(b) Find the population when t --> ∞. This is the steady -state population
(c) Solve for t and hence find the time at which the population is half of the steady-state value.
(d) Sketch the graph of P(t)

(a) DONE = P(0) = a/b+1
(b) DONE = P(∞)= a/b
(c) Can't do
(d) Can't do

Can someone help me do these please

 

[Riviet]

For (c), it asks to solve for t but you dont have enough information to find a numerical value for t, so i think it means to make t the subject of the formula:
P=a/b+e^-at
P-a/b=e^-at
ln(P-a/b)=-at
t=-ln(P-a/b)/a
for (d) it is basically an exponential decay curve shifted up by a/b units, label vertical axes P and horizontal axes t.
P.S I am not 100% sure that these hints are correct

 

[pLuvia]

so for (d) the curve is the normal exponential decay but just have the y int. a/b

 

[pLuvia]

Oh crap made a fatal mistake in typing the question out this one is the one it SHOULD be:

The population P of a certain kind of insects is given by P(t)= a/(b+e^-at), where a and b are positive constants.

(a) Find the initial population
(b) Find the population when t --> ∞. This is the steady -state population
(c) Solve for t and hence find the time at which the population is half of the steady-state value.
(d) Sketch the graph of P(t)

(a) DONE = P(0) = a/b+1
(b) DONE = P(∞)= a/b
(c) Can't do
(d) Can't do

Can someone help me do these please

 

[香港!]

ooo Riviet you play Final Fantasy 8!
What about the others?

 

[pLuvia]

Can someone help me instead of talking about FF8

 

[香港!]

hahaha, i would but im doing english @_@
wat help do u want?

 

[klaw]

you're not given enough info to do c, you need something like after x secs, P(x)=something

 

[pLuvia]

A, nevermind I figured it out myself lol.

That's all the information it gives

 

[Riviet]

ooo Riviet you play Final Fantasy 8!
What about the others?

Lol, i own FF8 and i've played 7, 9, X, and X2 at friend's place. FF7 has great plot, although my favourite overall is 8, X1 and X2 have great graphics and 9 was alright.