Question

The function f(t) = 6500(1.85)^365t represents the change in a quantity over t years. What does the constant 1.85 reveal about the rate of change of the quantity?

Answer 1

Here, we want to know what the constant reveal

The growth factor inside the bracket as can be seen is greater than 1

It can also be less than 1

When it is greater than 1, there is an indication of a positive change from year to year

1.85 is greater than 1 and as such, we have an indication for a positive change

That means, as the years roll by, there will be a greater value of the quantity

Hence, as t increases, f(t) increases

To find the percentage growth rate, we subtract 1 from the growth value which is (1.85-1) = 0.85

0.85 represents a percentage of 85%; and thus there is a growth rate of 85% per year