Question

the temperature, f(t) of a cup of coffee, in degrees celsius, after t minutes can be determined by the equation f(t) = 51(0.89)^t + 24. a graph of the function f(t) is shown below. estimate the temperature after 15 minutes

Explanation:

Step1: Identify the time value

We need to find the temperature at \( t = 15 \) minutes.

Step2: Analyze the graph

Looking at the graph, when \( t = 15 \), we check the \( f(t) \)-axis (y - axis) corresponding to \( t = 15 \) on the \( t \)-axis (x - axis). The graph at \( t = 15 \) seems to intersect the horizontal line around \( f(t)=32 \) (or we can also use the formula: \( f(15)=51(0.89)^{15}+24 \). First, calculate \( (0.89)^{15}\approx0.164 \), then \( 51\times0.164 = 8.364 \), and \( 8.364 + 24=32.364\approx32 \)).

Answer:

32 (or around 32, depending on the graph's precision)