Question

The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500 and its value increases at a rate of 5% per year. Find the value of the item after 4 years

Answer 1

Answer:

The value of the item after 4 years is $607.75

Step-by-step explanation:

* Lets revise the exponential function

- The original exponential formula was y = ab^x, where a is the initial

 amount and b is the growth factor

- The new growth and decay functions is y = a(1 ± r)^x. , the b value

 (growth factor) has been replaced either by (1 + r) or by (1 - r).

- The growth rate r is determined as b = 1 + r

* Lets solve the problem

- The value of a collector’s item is expected to increase exponentially

  each year, so we will yes the exponential equation y = a(1 + r)^x ,

  where y is the value of the item after x years

- The item is purchased for $500

∵ The initial amount is 500

∴ a = 500

- Its value increases at a rate of 5% per year

∵ The rate of increasing is 5% per year

∴ r = 5/100 = 0.05

- To find the value of the item after 4 years replace x by 4

∵ x = 4

∴ y = 500(1 + 0.05)^4

∴ y = 500(1.05)^4 = 607.75

∵ y is the value of the item after 4 years

∴ The value of the item after 4 years is $607.75

Answer 2

Answer:607.81

Step-by-step explanation:that’s what I got believe me on this one guys