last 2 for tonight
Express log6(19) in terms of common logarithms. Then approximate its value to four decimal places.
Answer:
log19/log6=1.6433
In a certain area, the sale price of new single-family homes has increased 4.1% per year since 1992. If a house was purchased in this area in 1992 for $75,000 and the growth continues, what will be the sale price in 2006? Use y=a(1+r)^t and round to the nearest cent.
Answer:
y=75,000(1+0.041)^14
y=75,000(1.041)^14
y=75,000(1.755)
y=$131625.00
Thanks
Express log6(19) in terms of common logarithms. Then approximate its value to four decimal places.
Answer:
log19/log6 Yes, did not check arithmetic
y=75,000(1+0.041)^14
y=75,000(1.041)^14
y=75,000(1.755)
y=$131625.00
I suppose, but given all the rest of the problems I bet you were supposed to do
14 log (1.041)
and then take the anti log instead of using the y^x key
To express log6(19) in terms of common logarithms, we can use the property of logarithms that allows us to change the base of the logarithm. The common logarithm has a base of 10, so we can rewrite log6(19) as log10(19) / log10(6).
To approximate the value of log10(19) / log10(6) to four decimal places, you can use a calculator or a computer program that has a logarithm function. Simply input 19, then take its logarithm to the base 10, and divide it by the logarithm of 6 to the base 10. The result is approximately 1.6433.
Now, let's move on to the second question regarding the sale price of new single-family homes in a certain area. We are told that the sale price has increased by 4.1% per year since 1992.
To find the sale price in 2006, we can use the compound interest formula y = a(1 + r)^t, where:
- y represents the final value or sale price we want to find,
- a represents the initial value or purchase price,
- r represents the growth rate per year (expressed as a decimal),
- t represents the number of years since the initial value.
In this case, the initial value or purchase price (a) is $75,000, the growth rate (r) is 4.1% or 0.041 (expressed as a decimal), and the number of years (t) is 2006 - 1992 = 14.
Plugging the values into the formula:
y = 75,000(1 + 0.041)^14
y ≈ 75,000(1.041)^14
y ≈ 75,000(1.755)
y ≈ $131,625.00 (rounded to the nearest cent)
Therefore, the sale price of the house in 2006 would be approximately $131,625.00.