Question

The amount of a radioactive element left after a certainnumber of hours can be determined by the functionA0(t) = A(1-P)^t where Ao is the initial amount of the element, t is the time in hours, and 0

Answer 1

In a exponential function of the form

y=a(1-r)^x

the term (1-r) represent the base of the exponential function

b=1-r

where r is the rate of change

In terms of this problem

1-p is less than 1

that means

is a exponential decay function -----> amount of a radioactive element left after a certain number of hours is decreasing

Part B

we have

A0=100 gr

For t=2 hours -------> A(t)=(36/100)*100=36 gr

substitute in teh equation

36=100(1-p)^2

36/100=(1-p)^2

square root both sides

6/10=1-p

p=1-0.6

p=0.40

therefore

the equation is

A(t)=100(0.40)^t

when A(t)=1 gr

substitute

1=100(0.40)^t

solve for t

1/100=0.40^t

Apply log both sides

log(1/100)=t*log(0.40)

t=5 hours