Question

An element with mass 570 grams decays by 26.9% per minute. How much of the element is remaining after 14 minutes, to the nearest 10th of a gram?

Answer 1

Answer:

element remained after 14 minutes = = 7.091 g =~ 10 g

Step-by-step explanation:

After every minute the amount remained will be

(100 - 26.9 ) % i.e. 73.1 %

which is 0.731 times as much as the amount was at the start.

if the number of minutes passed is represented by t the function f(t) represents the mass of element remaining our equation will be

f(t) = 570( 0.731) ^ t

t= 14 minutes

f(14) = 570 ( 0.731) ^ 14

      = 7.091 g =~ 10 g

Answer 2

Answer:

7.1

Step-by-step explanation:

Exponential Functions:

y=ab^x

y=ab  

x

 

a=\text{starting value = }570

a=starting value = 570

r=\text{rate = }26.9\% = 0.269

r=rate = 26.9%=0.269

\text{Exponential Decay:}

Exponential Decay:

b=1-r=1-0.269=0.731

b=1−r=1−0.269=0.731

\text{Write Exponential Function:}

Write Exponential Function:

y=570(0.731)^x

y=570(0.731)  

x

 

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=570(0.731)^{14}

y=570(0.731)  

14

 

y= 7.091174

y=7.091174

Evaluate

y\approx 7.1

y≈7.1

round