Word problem

[caligirl350]

The sales of a mature product (one which has passed its peak) are given by the function S(t) = S0e-at, where t is time in years. Find the sales after 19 years if a = 0.12 and S0 = 99,300.

so do I take the 0.12*99,300?

 

[JeffWest]

You are close. Thank you for showing what you did, it helps.


The problem gives you the formula. \(\displaystyle S(t)=S_0e^(^-^a^t^)\)


They Give you:
\(\displaystyle a=0.12\)
\(\displaystyle S_0=99,300\)

and they also give you t. t represents time in in this problem.
\(\displaystyle t=19\)

What you are looking for is \(\displaystyle S(t)\)

Plug in your numbers into the formula...then it gives you your answer.

One more thing the 'e' in the equation represents an exponential function. There is a button on you calculator for it. It should be near the log button.

If you get stuck keep showing us what you did. It helps.

 

[mmm4444bot]

Does the given function look like the following?

\(\displaystyle S(t) = S_0 \ e^{-at}\)

In other words, the product -a*t is an exponent?

If so, then substituting t = 19, a = 0.12 and S[sub:1ve2pkvi]0[/sub:1ve2pkvi] = 99300 looks like this:

\(\displaystyle S(19) = 99300 \ e^{-0.12(19)}\)

 

[caligirl350]

Thank you. 10,157 is what I came up with.