question\na motorcycle bought for $10,000 depreciates continuously at 9% per annum. what is its value after…

Explanation:

Step1: Identify the continuous - depreciation formula

The formula for continuous depreciation is $A = Pe^{-rt}$, where $P$ is the initial value, $r$ is the rate of depreciation, and $t$ is the time in years. Here, $P=$10000$, $r = 0.09$ (since $9%=0.09$), and $t = 7$.

Step2: Substitute the values into the formula

$A=10000e^{-(0.09\times7)}$. First, calculate the exponent: $0.09\times7 = 0.63$. Then, $A = 10000e^{- 0.63}$. We know that $e^{-0.63}=\frac{1}{e^{0.63}}$. Using a calculator, $e^{0.63}\approx1.8776$. So, $e^{-0.63}\approx\frac{1}{1.8776}\approx0.5326$.

Step3: Calculate the value of $A$

$A = 10000\times0.5326=5326$.

Answer:

$5,326$