Question

Exponential and Reciprocal Graphs - Question 5

Answer 1

a) P = (1, 1000)

b) $1,000

c) $2,488.32

Explanation:

We are given an exponential function and its graph and are asked to find certain values.

a) Coordinates of P

We can see that P is when t = 0. We will simplify substitute 0 for t into the given function.

`V = 1,000*1.2^t` ➜
`V = 1,000*1.2^0` ➜
`V = 1,000*1` ➜
`V = 1,000`

This gives us the point (1, 1000).

b) Value on January 1st of 2010

It is given that V is the value of the vase t years after January 1st of 2010. If we are being asked to find the value at this date, it will be the value of V when t = 0. We found this in part A.

`V = 1,000`

The value of the vase is $1,000.

c) Value on January 1st 2015

We will first find t. In other words, we will find how many years after 2010 the year 2015 is.

2015 - 2010 = 5, so t = 5

Next, we will substitute this in for t and solve for V.

`V = 1,000*1.2^5` ➜
`V = 1,000*2.48832` ➜
`V = 2,488.32`

The value of the vase is $2,488.32.