Assume an exponential function has a starting value of 19 and a decay rate of ​30%. Write an equation to model the situation.

Question

Assume an exponential function has a starting value of 19 and a decay rate of ​30%. Write an equation to model the situation.

Answer 1

A(t) = 19e^-.3t

A = ending Amount

19 = starting amount

e = about 2.718281828... an irrational number

t = number of years

.3 = decay rate = 30%

or

A(t) = 19(1+ r/n)^nt

= 19(1 + .3/n)^nt

where t = number of compounding periods per year

as compounding periods approach infinity, the formula A=P(1+r/n)^nt

approaches A = Pe^rt

Answer 2

If 30% is lost, I'm left with 70%, right?

After one period, I am left with 19(0.7). After 2 periods, I'm left with 19(0.7)(0.7).

Let t = one period of time.

f(t) = 19(0.7)^t