Question

the function $f(t) = 349.2(0.98)^t$ models the relationship between $t$, the time an oven spends cooling and the temperature of the oven.

oven cooling time

time (minutes) $t$	oven temperature (degrees fahrenheit) $f(t)$
10	285
15	260
20	235
25	210

for which temperature will the model most accurately predict the time spent cooling?

• 0
• 100
• 300
• 400

Explanation:

Step1: Analyze the function \( f(t)=349.2(0.98)^{t} \)

This is an exponential decay function. When \( t = 0 \), \( f(0)=349.2(0.98)^{0}=349.2\times1 = 349.2 \). As \( t \) increases, \( f(t) \) decreases.

Step2: Check the given data points

When \( t = 5 \), \( f(5)=349.2(0.98)^{5}\approx349.2\times0.9039 = 315 \) (matches the table). When \( t = 10 \), \( f(10)=349.2(0.98)^{10}\approx349.2\times0.8171=285 \) (matches the table). The values in the table are close to the function values for \( t = 5,10,\cdots \). The function is defined for \( t\geq0 \). The initial value of the function \( f(0) = 349.2 \) is close to \( 300 \) (compared to \( 0,100,400 \)). Since the function is an exponential model, it is more accurate for values near the initial - modeled range.

Answer:

300