The amount of carbon dioxide (\text{CO}_2)(CO 2 )left parenthesis, start text, C, O, end text, start subscript, 2, end subscri
pt, right parenthesis in the atmosphere increases rapidly as we continue to rely on fossil fuels. The relationship between the elapsed time, ttt, in decades, since \text{CO}_2CO 2 start text, C, O, end text, start subscript, 2, end subscript levels were first measured, and the total amount of \text{CO}_2CO 2 start text, C, O, end text, start subscript, 2, end subscript in the atmosphere, A_{\text{decade}}(t)A decade (t)A, start subscript, start text, d, e, c, a, d, e, end text, end subscript, left parenthesis, t, right parenthesis, in parts per million, is modeled by the following function:
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Answer:
The resulting graph is .
Step-by-step explanation:
The resulting function is of the form:
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Amplitude, dimensionless.
- Midpoint value, dimensionless.
The sine function is bounded, between -1 and 1, and must be multiplied by a stretch factor. That is: . According to the graph, the function is bounded between 5 (
) and -5 (
), and the midpoint value (
) is 0. The amplitude is determined by the following calculation:
If and
, then:
The resulting graph is .