Question

Assume an exponential function has a starting value of 16 and a decay rate of 0.52%. Write an equation to model the situation.

Answer 1

`A(t)=16(0.99948)^t`

Explanation:

The exponential function is modeled using the equation:

`A(t)=A_o(1\pm r)^t`

Where the plus sign indicates growth and the negative sign indicates exponential decay.

• r=Decay/Growth constant
• t=time
• 
  `A_0` is the starting value.

For an exponential function has a starting value of 16 and a decay rate of 0.52%.

`A_0=16\\r=0.052\%=0.00052`

This gives:

`A(t)=16(1- 0.00052)^t\\A(t)=16(0.99948)^t`

The function that models this situation is:

`A(t)=16(0.99948)^t`