What is the exponential function with a concave up graph and two given points?

[JonF]

I have no idea how to do this problem or where to even start: Find the exponential function f(x) = Ca^x who’s graph is given. The graph has a concave up line, that intersects the y-axis at what looks like ½ (no exact intersection is given) and has the two points (1,6) and (3,24).

 

[Muzza]

That the point (1, 6) lies on the graph means that f(1) = 6. But f(x) = Ca^x, so f(1) = Ca^1 = Ca = 6. You can find a similar equation using the other point. You now have two equations and two unknowns. Can you take it from there?

 

[HallsofIvy]

However, the graph of y= Ca^x, passing through (1,6) and (3,24) doesn't cross the y-axis anywhere near 1/2!

 

[Gokul43201]

However, the graph of y= Ca^x, passing through (1,6) and (3,24) doesn't cross the y-axis anywhere near 1/2!

It crosses at y=3/2.

 

[JonF]

That helps a lot, thank you. Sorry about the ½ thing, didn’t do a very good job of eyeballing it.