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
