On 1st January 1900, a sculpture was valued at £80. When the sculpture was sold on 1st January 1956, its value was £5000.
The value, £V, of the sculpture is modelled by the formula V = Ak', where t is the time in
years since 1st January 1900 and A and k are constants.
a) Use this model to show that the value of the sculpture on 1 January 2006 will be
greater than £200 000.

b) Find the year in which the value of the sculpture on the 1st January will first exceed
£800 000.

3030 ur welcome

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1