Question

a chemical substance has a decay rate of 7.3% per day. the rate of change of an amount n of the chemical after t days is given by $\frac{dn}{dt}=-0.073n$. a) let $n_0$ represent the amount of the substance present at $t = 0$. find the exponential function that models the decay. b) suppose that 600 g of the substance is present at $t = 0$. how much will remain after 5 days? c) what is the rate of change of the amount of the substance after 5 days? d) after how many days will half of the original 600 g of the substance remain? a) $n(t)=n_0e^{-0.073t}$. b) after 5 days, $square$ g will remain. (round to the nearest whole number as needed.)

Explanation:

Step1: Identify the values for the decay - formula

We know that $N_0 = 600$ (initial amount) and the decay formula is $N(t)=N_0e^{-0.073t}$.

Step2: Substitute $t = 5$ into the formula

Substitute $N_0 = 600$ and $t = 5$ into $N(t)=N_0e^{-0.073t}$, we get $N(5)=600e^{-0.073\times5}$.
First, calculate the exponent: $-0.073\times5=-0.365$.
Then, find the value of $e^{-0.365}\approx0.6947$.
Finally, $N(5)=600\times0.6947 = 416.82\approx417$.

Answer:

417