Question

Consider the exponential function below and determine which one of the following statements is true. p(t)=800(0.7)���. p describes exponential decay where the initial quantity is 800. p describes exponential growth where the initial quantity is 800. p describes exponential decay where the initial quantity is 0.7. p describes exponential growth where the initial quantity is 0.7?

1) p describes exponential decay where the initial quantity is 800.
2) p describes exponential growth where the initial quantity is 800.
3) p describes exponential decay where the initial quantity is 0.7.
4) p describes exponential growth where the initial quantity is 0.7.

Answer 1

The function p(t) = 800(0.7)^t describes exponential decay, not exponential growth, with an initial quantity of 800 because the base of the exponent (0.7) is less than 1, indicating that the value of p(t) decreases as time increases.

Step-by-step explanation:

The function given is p(t) = 800(0.7)^t. This is an exponential function, which represents either growth or decay. The base of the exponent (0.7) in this function is less than 1, indicating that the function represents exponential decay. As time increases, the quantity p(t) decreases. The initial quantity, given by the coefficient in front of the exponential expression, is 800. Therefore, the correct statement is that p describes exponential decay where the initial quantity is 800.