3 years ago

Allison car can drive 450 miles on just 12 gallons of gas what is the mileage per gallon

Mathematics

1 answer:

kirza4 [7]3 years ago

4 0

37.5 if you divide 450 by 12

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Answer:

Present value = $4,122.4

Accumulated amount = $4,742

Step-by-step explanation:

Data provided in the question:

Amount at the Start of money flow = $1,000

Increase in amount is exponentially at the rate of 5% per year

Time = 4 years

Interest rate = 3.5% compounded continuously

Now,

Accumulated Value of the money flow = $1000e^{0.05t}$

The present value of the money flow = $\int\limits^4_0 {1000e^{0.05t}(e^{-0.035t})} \, dt$

= $1000\int\limits^4_0 {e^{0.015t}} \, dt$

= $1000\left [\frac{e^{0.015t}}{0.015} \right ]_0^4$

= $1000\times\left [\frac{e^{0.015(4)}}{0.015} -\frac{e^{0.015(0)}}{0.015} \right]$

= 1000 × [70.7891 - 66.6667]

= $4,122.4

Accumulated interest = $e^{rt}\int\limits^4_0 {1000e^{0.05t}(e^{-0.035t}} \, dt$

= $e^{0.035\times4}\times4,122.4$

= $4,742

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