Question

A tank is draining water such that the volume is given which an exponentially decreasing graph as shown in the graph below. If the volume was modeled with an equation of the form V=a(b)^t, where t is the number of hours then which of the following is the best value for b?

(1) b=20
(2) b=0.6
(3) b=2.8
(4) b=0.3

Answer 1

`b = 0.3`

Explanation:

Given

`V = ab^t`

See attachment for graph

From the graph

V = 20 when t = 0

This implies that:

`V = ab^t`

`20 = ab^0`

`20 = a * 1`

`20 = a`

`a = 20`

Also:

V = 4 when t = 1.5

So:

`4 = ab^{1.5`

Substitute 20 for a

`4 = 20 * b^{1.5`

Divide by 20

`0.2 =b^{1.5`

`b^(1.5) = 0.2`

Take 1.5th root of both sides

`b = 0.34199518933`

`b = 0.3` --- approximated