Question

The concentration of a pollutant in a lake is 85 parts per million (ppm) and is increasing at a rate of 4.6% each year. A possible formula for the concentration C as a function of year tis:

(a) C 85 +4.6t
(b) C-85-4.6t .
(c) C-85 +0.046t
(d) C-85 -0.046
(e) C = 85 (0.046)
(f) C-85 (0.954)
(g) C = 85 (1.046)
(h) C-85(1.46)
(i) C85(0.46)
(j) C-4.6 (0.85)

Answer 1

`C(t) = 85(1.046)^t`, and the correct answer is given by option g.

Explanation:

Equation for an concentration increasing exponentially:

The concentration after t years, considering that it increases exponentially, is given by the following equation:

`C(t) = C(0)(1 + r)^t`

In which C(0) is the initial concentration and r is the growth rate, as a decimal.

The concentration of a pollutant in a lake is 85 parts per million (ppm) and is increasing at a rate of 4.6% each year.

This means that
`A(0) = 85, r = 0.046`. Thus

`C(t) = C(0)(1 + r)^t`

`C(t) = 85(1 + 0.046)^t`

`C(t) = 85(1.046)^t`, and the correct answer is given by option g.