what is the equation of an exponential growth function, crossing points (0,0) and (1,3) with a horizontal asymptote at y=6?

Question

I need to know the function's equation 

Answer 1

Hi Caitlyn, this is a long problem but keep trying and it'll work out.

 

let the function be:

 y = be^ax+c 

 

since, horizontal asymptote at y= 6, c = 6

plug in both points into original equation:

 

at (0,0)

0 = be⁰ + 6 

b = -6

 

at (1,3)

3 = -6e^a*1 +6

a = -ln2

 

final equation should then be:

 

y = -6 e^-xln2 + 6

 

recall        a*lnx ≡ lnx^a

y =  -6e^(ln2^-x) +6

 

recall e^lna = a

y = -6(2^-x) +6 

 

Always make the habit of checking your solution with the points given.