To write an exponential function for the graph, we can use the general formula for exponential decay:
y = a * (1 - r)^x
where:
- y is the value of the boat at a certain number of years (x)
- a is the initial value of the boat ($3500 in this case)
- r is the rate of decay
- x is the number of years
From the graph, we can see that the value of the boat after 1 year is approximately $2700. Substituting this information into the formula, we get:
2700 = 3500 * (1 - r)^1
Solving for r:
2700 = 3500 * (1 - r)
0.7714 = 1 - r
r = 0.2286
Therefore, the exponential function for the graph is:
y = 3500 * (1 - 0.2286)^x
Now, to find the value of the boat after 9.5 years:
y = 3500 * (1 - 0.2286)^9.5
y = 3500 * (0.7714)^9.5
y ≈ 1684.74
Therefore, the value of the boat after 9.5 years is approximately $1684.74.
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The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years.
A coordinate graph is shown. The horizontal axis extends from 0 to 12 years. The vertical axis extends from 0 to 9500 with an axis label of 'Value' in dollars. A curve is graphed which begins at 0 comma 3500, then decreases passing through approximately 1 comma 2700
Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years.
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