suppose a house that costs $270,000 appreciates by 5% each year. in about how many years will the house be worth $350,000? use the equation 350 = (270) (1.05)^x and round the value of x to the nearest year.
To find the number of years it will take for the house to be worth $350,000, we can use the equation you provided: 350,000 = 270,000 (1.05)^x.
Let's solve for x:
350,000 / 270,000 = (1.05)^x
1.2963 = (1.05)^x
To find the value of x, we need to take the logarithm of both sides of the equation. Let's use the natural logarithm (ln) for this calculation:
ln(1.2963) = ln((1.05)^x)
x(ln(1.05)) = ln(1.2963)
Now we can isolate x by dividing both sides by ln(1.05):
x = ln(1.2963) / ln(1.05)
Using a calculator to evaluate this:
x ≈ 5.21
Rounding to the nearest year, we get:
x ≈ 5 years
Therefore, it will take approximately 5 years for the house to be worth $350,000.
To solve the equation 350 = 270(1.05)^x for x, we need to isolate the variable x.
Starting with the equation:
350 = 270(1.05)^x
Divide both sides of the equation by 270:
350/270 = (1.05)^x
Simplify:
1.2963 ≈ (1.05)^x
To solve for x, we can take the logarithm of both sides of the equation. Let's use the natural logarithm (ln) for this example:
ln(1.2963) = ln((1.05)^x)
Simplify using the rule of logarithm:
ln(1.2963) = x * ln(1.05)
Now, we can isolate x by dividing both sides of the equation by ln(1.05):
ln(1.2963) / ln(1.05) = x
Using a calculator, evaluate the left side of the equation:
x ≈ 8.45
Rounding this value to the nearest year, we can conclude that it will take approximately 8 years for the house to be worth $350,000.
89
350 = (270) (1.05)^x
1.2963 = 1.05^x
log both sides
log 1.2963 = log (1.05^x)
log 1.2963 = xlog(1.05)
x = log1.2963/log1.05
= ....
you do the button pushing.