Question

An element with mass 570 grams decays by 18% per minute. How much of the element is remaining after 13 minutes, to the nearest 10th of a gram?

Answer 1

Given :

The mass of element = m = 570 grams

The rate of decay of element = r = 18% per min

Time for decay = t = 12 min

To Find :

The mass of element remaining after 13 minutes

Solution :

Let The mass of element remaining after 13 minutes = A grams

According to question

Amount after 13 min = initial amount × $(1-\dfrac{rate}{100})^{time}$

Or,  A = m ×$(1-\dfrac{r}{100})^{t}$

Or, A = 570 grams  ×$(1-\dfrac{18}{100})^{12}$

Or, A = 570 grams  × $(0.82)^{12}$

Or, A = 570 grams  × 0.09242

∴ Amount after 13 min = A = 52.67 grams

Hence, The Amount of elements after 13 min of decay is 52.67 grams Answer

Answer 2

Answer:

An element with mass 570 grams decays by 18% per minute. How much of the element is remaining after 13 minutes, to the nearest 10th of a gram?

\text{Exponential Functions:}

Exponential Functions:

y=ab^x

y=ab  

x

 

a=\text{starting value = }570

a=starting value = 570

r=\text{rate = }18\% = 0.18

r=rate = 18%=0.18

\text{Exponential Decay:}

Exponential Decay:

b=1-r=1-0.18=0.82

b=1−r=1−0.18=0.82

\text{Write Exponential Function:}

Write Exponential Function:

y=570(0.82)^x

y=570(0.82)  

x

 

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=570(0.82)^{13}

y=570(0.82)  

13

 

y= 43.197134

y=43.197134

Evaluate

y\approx 43.2

y≈43.2

Step-by-step explanation: