Question

As time, t, passes, the value of an investment is modeled by the function: V(t)=50(0.9)t

Which of the following statements is supported by the behavior of V(t)?


A.) The value of the investment will decrease over time.

B.) No generalizations can be made because the value of the investment will both increase and decrease over time.

C.) The value of the investment will increase over time.

D.) The value of the investment will remain the same.

Answer 1

Answer:

Step-by-step explanation:

Since what is in the parenthesis is less than 1 that means that whatever the answer is should be less than what you started with and you should get a answer of 45

Answer 2

Answer:

A) The value of the investment will decrease over time.

Step-by-step explanation:

Since, the function that shows the value of investment after t time,

$V(t)=50(0.9)^t$

Which is an exponential function,

There are two type of exponential function,

Growth : If in the function $y=ab^x$

b > 1

Decay :  If in the function $y=ab^x$

0 < b < 1

Here, b = 0.9 which is between 0 and 1,

Hence, the given function is exponential decay function,

Therefore, the value of the investment will decrease over time,

Option 'A' is correct.