Exponential Decay

[bro123]

Hi Everyone,

The question states, Consider the following graph of the exponential decay of the form f(x)=be^(-ax)+c for some b, c, and a >0. What are the values of a, b, and c? Hence find the equation of the graph.
The graph should be attached below it was an asymptote of y=20 the graph intercepts the y axis at (0,22.5) and a point on the graph is (1,20.616).



I believe that b is 22.5 and possibly c is 20.161 but I am not 100% sure, your help would be much appreciated!

Thanks in advance

 

[Harry_the_cat]

Consider the graph of f(x) = be^(-ax). This would have a horizontal axis at y=0. But this graph has a horizontal axis at y=20. This suggests that the vertical shift c=?

Once you have found c, use the fact that f(0)=22.5 to find b.

Then use the other given point to find a.

Give it a go. Come back if you need help. let us know what you get.

 

[bro123]

Consider the graph of f(x) = be^(-ax). This would have a horizontal axis at y=0. But this graph has a horizontal axis at y=20. This suggests that the vertical shift c=?

Once you have found c, use the fact that f(0)=22.5 to find b.

Then use the other given point to find a.

Give it a go. Come back if you need help. let us know what you get.

i got f(x)=2.5e^(-1.4x)+20
thanks so much for the help really appreciate it!!!

 

[Cubist]

I suspect that you might get full marks for your answer in post#3.

However it might be better to summarise with:-
a≈1.4
b=2.5
c=20
...this shows, with the wavy equal line, that the value of a has been rounded