the plot in the tb - plane shows the brewing time, b, defined as the time it takes for a tea packet to reach…
the plot in the tb - plane shows the brewing time, b, defined as the time it takes for a tea packet to reach a caffeine concentration of 100 milligrams per liter with water at a temperature of t degrees celsius. which of the following equations best models the relationship between b and t? choose 1 answer. b = 9 - 0.66^t b = 9 - 0.06^t b = 25 - 0.66^t b = 25 - 0.06^t
Answer
Explanation:
Step1: Analyze the trend of the data points
The data points show a decreasing - exponential relationship between (B) (brewing time) and (T) (temperature). The general form of an exponential decay function is (y = a\cdot b^{x}), where (0 < b<1). When (x = 0), (y=a).
Step2: Estimate the (y) - intercept
When (T = 0), from the graph, (B) is approximately (9). So, the value of (a) in the function (B=a\cdot b^{T}) is around (9).
Step3: Analyze the decay factor
As (T) increases, (B) decreases. We need to find a value of (b) such that the function fits the data. Since the decay is not too rapid, we can eliminate options with very small (b) values.
Step4: Check the options
For an exponential - decay function (B=a\cdot b^{T}), when (a = 9) and considering the decay rate of the data points, the function (B = 9\cdot0.96^{T}) is a reasonable fit. The function (B = 9\cdot0.66^{T}) would decay too rapidly, and functions with (a = 25) are not consistent with the (y) - intercept of the graph.
Answer:
B. (B = 9\cdot0.96^{T})