Question

The function f, of, t, equals, 6800, left parenthesis, 1, point, 6, 5, right parenthesis, start superscript, start fraction, t, divided by, 365, end fraction, end superscriptf(t)=6800(1.65)
365
t
​

represents the change in a quantity over t years. What does the constant 1.65 reveal about the rate of change of the quantity?
Answer
Attempt 1 out of 2

The function is
exponentially at a rate of
% every
.

Answer 1

The function \( f(t) = 6800(1.65)^{\frac{t}{365}} \) describes exponential growth, where the base \( 1.65 \) indicates the growth factor over the period of one year.

To determine the annual growth rate, we can follow these steps:

1. The growth factor \( 1.65 \) means that after one full year (365 days), the quantity will multiply by \( 1.65 \), indicating a growth of \( 0.65 \) or \( 65\% \) over the year.

2. To express it as a percentage, we can subtract 1 from our growth factor (to find just the growth portion) and multiply by 100:
\[
(1.65 - 1) \times 100 = 0.65 \times 100 = 65\%
\]

Based on this information, we can conclude:

**The function is growing exponentially at a rate of 65% every year.**