The following table gives the value of an investment, after intervals ranging fr

Question

The following table gives the value of an investment, after intervals ranging from 0 to 7 years, of $40,000 invested at 10%, compounded annually. Year Amount Investment Grows to 40,000.00 44,000.00 48,400.00 53,240.00 58,564.00 64,420.40 70,862.44 77,948.68 2 4 6 (a) Develop an exponential model for these data, accurate to four decimal places, with x in years and y in dollars (b) Use the model to find the amount to which s40,000 will grow in 38 years if it is invested at 10%, compounded annually. (Round your answer to two decimal place Need Help? Readt Show My Work (optional) + -/1 points HarMathAp11 5.2.041 Use the properties of logarithms to write the expression as a single logarithm In(6x) In(6y) Need Help? Read ItWatch It a Show My Work (optional t-1 points HarMathAp11 5.2 064 Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to L = 10 log(I/10) where lo is the threshold of hearing for the average human ear. A sound that causes pain has intensity about 1014 times . Find the decibel reading for this threshold dB

Explanation / Answer

1) standard exponnetial function is

y = ab^x

plugging 1st value from data

40,000 = ab^0

a = 40,000

44000 = ab

44000/40000 = b

b = 1.1

hence, the function is

y = 40,000(1.1)^x

b) plugging x = 38

y = 40,000 ( 1.1)^38

y = 1496173.74

= $ 1496173.74

2) ln (6x) - ln (6y)

using properties of logarithm

ln ( 6x / 6y )

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