Exponential Functions

Question

Certain radioactive material decays in such a way that the mass remaining after t years is given by the function 

m(t)=170e−0.025t

where m(t) is measured in grams. 

a) Find the mass at time t=0

b)How much of the mass remains after 45 years? 

Round answers to 1 decimal place.

Answer 1

I'm going to assume the function is:

m(t)=170e^−0.025t

At time t = 0 we have:

m(0)=170e^−0.025•0

m(0)=170e⁰

Since anything (except zero) raised to the zero power is equal to one, then

m(0)=170(1) = 170 grams

After 45 years:

m(45)=170e^{−0.025•45}

m(45)=170e⁻¹

since a number raised to a negative power is equal to one over the number raised to a positive power of the same amount then:

m(45)=170•(1/e¹) = 170•(1/e) = 170/e = 62.5 grams