Question

An element with a mass of 550 grams decays by 18.8% per minute. To the nearest minute, how long will it be until there are 60 grams of the element remaining

Answer 1

Answer:  11

Step-by-step explanation:

Exponential Functions:

y=ab^x

y=ab  

x

 

a=\text{starting value = }550

a=starting value = 550

r=\text{rate = }18.8\% = 0.188

r=rate = 18.8%=0.188

\text{Exponential Decay:}

Exponential Decay:

b=1-r=1-0.188=0.812

b=1−r=1−0.188=0.812

\text{Write Exponential Function:}

Write Exponential Function:

y=550(0.812)^x

y=550(0.812)  

x

 

Put it all together

\text{Plug in y-value:}

Plug in y-value:

60=550(0.812)^x

60=550(0.812)  

x

 

\frac{60}{550}=\frac{550(0.812)^x}{550}

550

60

​  

=  

550

550(0.812)  

x

 

​  

 

Divide both sides by 550

0.109091=0.812^x

0.109091=0.812  

x

 

\log 0.109091=\log 0.812^x

log0.109091=log0.812  

x

 

Take the log of both sides

\log 0.109091=x\log 0.812

log0.109091=xlog0.812

use power rule to bring x to the front

\frac{\log 0.109091}{\log 0.812}=\frac{x\log 0.812}{\log 0.812}

log0.812

log0.109091

​  

=  

log0.812

xlog0.812

​  

 

Divide both sides by log(0.812)

10.638757=x

10.638757=x

x\approx 11

x≈11