a cup of hot water is left out to cool. the water is currently 19°c above room temperature. if the heat…

a cup of hot water is left out to cool. the water is currently 19°c above room temperature. if the heat difference decreases by 5% every minute, what will the difference be in 13 minutes? if necessary, round your answer to the nearest tenth. °c

a cup of hot water is left out to cool. the water is currently 19°c above room temperature. if the heat difference decreases by 5% every minute, what will the difference be in 13 minutes? if necessary, round your answer to the nearest tenth. °c

Answer

Explanation:

Step1: Identify the formula

This is an exponential - decay problem. The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $P = 19$, $r=0.05$, and $t = 13$.

Step2: Substitute the values into the formula

$A=19\times(1 - 0.05)^{13}$. First, calculate $(1 - 0.05)=0.95$. Then, find $0.95^{13}$. Using a calculator, $0.95^{13}\approx0.513$.

Step3: Calculate the final value

$A = 19\times0.513$. $A\approx9.8$.

Answer:

$9.8$