Bernice is selling seashells she has found at the beach. The price of shell depends on the length of the shell.

Cm 5 8 12 20 25
Price ($) 2 3.5 5 18 40

A.)find the exponential model for the data
B.)what is the length of a shell selling for 9$
C.)40cm conch shell should sell for him much?

Question

Bernice is selling seashells she has found at the beach. The price of shell depends on the length of the shell.

Cm 5 8 12 20 25
Price ($) 2 3.5 5 18 40

A.)find the exponential model for the data
B.)what is the length of a shell selling for 9$
C.)40cm conch shell should sell for him much?

mathmale · Answer

It's important to know the basic form of the "exponential model."  While y=e^x is the simplest form, in approaching a problem such as this one, I prefer y=a*e^(bx), where a and b are constants to be determined.

anonymous · Answer

So what would A and B represent?

mathmale · Answer

We can assume that this data does follow an exponential model:  the problem statement asks us to find such a model.

We have two unknowns, a and b, in this model.

To find a and b, we need to develop two simultaneous equations in a and b.  Pick any two x values in the given table, along with the corresponding y values.  For example, pick (8,3.5) and (25,40).  Write out y=a*e^(bx) in each case, substituting the relevant x for a and the relevant y for b.  For example:  y=a*e^(bx) becomes 3.5=a*e(8b).

Solve the resulting system of two equations in the two unknowns, a and b.  Substitution will probably prove to be the easiest way of doing this.

anonymous · Answer

Ok that makes sense,thanks for being patient!

mathmale · Answer

a represents the value y would have if x were = to zero:  y=a*e^0.
b in this case would be called the "exponential growth constant;" it has to do with how fast y increases as x increases.

mathmale · Answer

Happy to work with you!

anonymous · Answer

That's exactly what I'm learning,great!