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

Answer:

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

Step-by-step 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:

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