Question

The function f(t)=5600(1.006)^{10t}f(t)=5600(1.006) 10t represents the change in a quantity over decades. What does the constant 1.006 reveal about the rate of change of the quantity?

Answer 1

If
`r = 1.006`, then it means that dependent variables increases by a factor of 1.006 per decade.

Explanation:

Mathematically speaking, the function represents an exponential equation, whose form is:

`f(t) = a_(o)\cdot r^(k\cdot t)` (1)

Where:

`t` - Independent variable.

`r(t)` - Dependent variable.

`a_(o)` - Initial value.

`k` - Convergence ratio.

`r` - Increase rate.

If
`r = 1.006`, then it means that dependent variables increases by a factor of 1.006 per decade.