#95 Mrs. Powell's art collection has been increasing in value by 8% per year. This year it was valued at $10,000.

Question

#95  Mrs. Powell's art collection has been increasing in value by 8% per year.  This year it was valued at $10,000.
(a)  Write an exponential equation for the value V of the collection t years from now.
(b)  What will the collection be worth 10 years from now?
(c)  When will the collection double in value?
(d)  How long will it take the value to double again?

could someone help me with this one, please ?

Answer 1

So, Norma, let's say I buy a t-shirt for $5 plus 8% tax. Normally, I would multiply 5(.08) = .4 and add 40 cents to the $5 for a total cost of $5.40.

 

Another way to look at it, though, is that if we add 8% to the price, we now have 108% of the price. $5(1.08) = $5.40.

 

If we apply that to continual appreciation or depreciation, every year, the NEW amount gets multiplied by the full percent.

 

Let's look at your problem. We have currently something worth $10,000 that appreciates every year.

 

$10,000(1.08) = $10,800 will be the value next year. $10,800(1.08) = $11,664, etc.

 

So, two years from now, it will be worth $10,000(1.08)(1.08), or $10,000(1.08)². After t years, it will be worth $10,000(1.08)^t.

 

Plug in 10 for t in your calculator for that answer.

 

It will double in value when $20,000, = $10,000(1.08)^t.

 

1.08^t = 2

log(1.08^t) = log(2)

tlog(1.08) = log(2)

t = log(2)/log(1.08)

Plug it in your calculator for an answer.

 

Replace $20,000 with $40,000 for d.