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: 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