The equation A= 27500(0.73)^t is a model of exponential decay. This can be determined because the base of the exponent, 0.73, is less than 1. In exponential decay, the value of the function decreases over time.
The rate of change per time period can be calculated by taking the derivative of the function with respect to time, t. The derivative of A= 27500(0.73)^t is given by:
dA/dt = 27500(0.73)^t * ln(0.73)
The rate of change per time period is the derivative of the function, which in this case would be:
dA/dt = 27500(0.73)^t * ln(0.73) ≈ -9826.31(0.73)^t
Therefore, the rate of change per time period is approximately -9826.31(0.73)^t. This means that the value of the function decreases by approximately 9826.31 units for each time period t.
Is the equation A= 27500(0.73)^t a model of exponential growth or exponential decay, and what is the rate of change per time period?
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