Sports store is having a closing down sale, all stock has to be sold. each day an article remains unsold, the price is discounted by 4% of the previous days price. This discounting continues until the article is sold. The table shows the price of a mountain bike during the first 5 days of the sale:

Day 1 = 750
Day 2 = 720
Day 3 = 691.20
Day 4 = 663.55
Day 5 = 637.01

A) State the growth factor

720/750 = 0.96

B) Calculate the cost of the mountain bike on the 10th day of the sale.

T10 = 750(0.96)^10-1
= 750(0.96)^9
750(0.69253) = 519.40

C) Write an expression for the cost of the mountain bike on the nth day of the sale:

$750(0.96)^n-1

D) The mountain bike was eventually sold for $359.70. On which day of the sale was it sold?

I don't get how to solve this one.

For D)

look at the log portion of this post,
I believe it was your post, but I can't tell since you continue to use "anonymous" for your name.

http://www.jiskha.com/display.cgi?id=1316650359

The bike was sold on the 19th day

359.70=750(0.96)^n-1
divide both sides by 750
0.4796=0.96^n-1
now just guess and check for n
0.4796=0.96^20-1
0.4796=0.4604
nope
0.4796=0.96^19-1
0.4796=4796
yep it works

n=19
so the bike was sold on the 19th day of the sale.
:)

To determine on which day the mountain bike was sold for $359.70, we can set up an equation using the expression for the cost of the bike on the nth day:

$750(0.96)^n-1 = $359.70

To solve for n, we can divide both sides of the equation by $750:

(0.96)^n-1 = $359.70 / $750

Simplifying the right side:

(0.96)^n-1 = 0.4796

To isolate the exponent, we can take the logarithm of both sides of the equation. Let's use the natural logarithm (ln):

ln[(0.96)^n-1] = ln(0.4796)

Using the properties of logarithms, we can bring down the exponent:

(n-1)ln(0.96) = ln(0.4796)

Now, we can solve for n by isolating it:

n - 1 = ln(0.4796) / ln(0.96)

n = ln(0.4796) / ln(0.96) + 1

Using a calculator, we can evaluate this expression:

n ≈ 12.69

Since the number of days must be a whole number, we can conclude that the mountain bike was sold on the 13th day of the sale.

To solve for the day on which the mountain bike was sold, we need to reverse-engineer the equation and solve for "n" in the expression for the cost of the bike on the nth day.

The expression for the cost of the mountain bike on the nth day is given as $750(0.96)^(n-1). We will set this expression equal to the selling price of $359.70 and solve for "n".

$750(0.96)^(n-1) = $359.70

To solve this equation, we can divide both sides by $750:

(0.96)^(n-1) = $359.70 / $750
(0.96)^(n-1) = 0.4796

Now, we need to take the logarithm (base 0.96) of both sides to solve for (n-1):

logbase0.96(0.96)^(n-1) = logbase0.96(0.4796)
(n-1) = logbase0.96(0.4796)

Using the logarithm rule logbaseb(b^x) = x, we can simplify further:

(n-1) = logbase0.96(0.4796)
(n-1) = -0.7918

To isolate "n", we add 1 to both sides:

n = -0.7918 + 1
n = 0.2082

So, the mountain bike was sold on the 0.2082 th day of the sale. Since days cannot be fractional, we can conclude that the bike was sold on the first day of the sale.