Fill in the blanks to solve the pollution problem.

• what do you want to know?

when the pollution level in the lake will reach 50 tons

• what do you know?

the exponential growth function that models the
problem is p(t) = 3 • e^0.0866t, where p(t) = the number
of tons of in the lake t after 1970.

The names/values/units in the blanks define the meaning of the function. Without knowing what this function is supposed to be modeling, the content of the blanks could be anything you like. (bacteria, decades), (water molecules, centuries)

If the "Pollution problem" has to do with tons of pollution and the way that amount increases over the years, then the descriptive words might be
.. (pollution, years)

_____
If you actually want to know when the pollution level will be 50 tons, this can be solved a couple of ways.

1) graph the function
.. f(x) = 3*e^(0.0866x) -50
and find the value of x that makes f(x) = 0.
That value is x = 32.487, so the pollution level will reach 50 tons in 2002.

2) Find t that satisfies P(t) = 50.
.. 50 = 3*e^(0.0866t)
.. 50/3 = e^(0.0866t) . . . . .divide by 3 to isolate the exponential term
.. ln(50/3) = 0.0866t . . . . . take the natural log
.. ln(50/3)/0.0866 = t ≈ 32.487
Write the answer in terms of a year number.
.. The pollution level will reach 50 tons in 1970+32 years, 2002.

Bis your answer. it only holds the decimal numerals