Mike and Beatrice purchase a house for $200,000. If the equation V = 200,000(1.03)x represents the value of the house after x years, how many years will it take the house to be worth approximately $225,000?

A4 years
B5 years
C6 years
D7 years

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Answered

Verified Answer :

irspow irspow · Answer 1 · 2017-03-22T11:38:10-04:00

225000=200000(1.03^t)

9/8=1.03^t

ln(9/8)=tln(1.03)

t=ln(9/8)/ln(1.03)

t=3.98

t=4 years

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wifilethbridge wifilethbridge · Answer 2 · 2019-02-25T13:52:25-05:00

Answer:

Option A - 4 years

Step-by-step explanation:

Given : Mike and Beatrice purchase a house for $200,000. If the equation @@MATH_TOKEN_0@@ represents the value of the house after x years.

To find : How many years will it take the house to be worth approximately $225,000?

Solution :

The given equation is $V = 200000(1.03)^x$

x is the number of years and V is the price of house.

In how many years the price became $225,000

V=$225,000

Substitute in the equation,

$V = 200000(1.03)^x$

$225000 = 200000(1.03)^x$

$\frac{225000}{200000}=(1.03)^x$

$1.125=(1.03)^x$

Taking log both side,

$\log(1.125)=\log((1.03)^x)$

Apply logarithmic formula, $\log(a)^x=x\log(a)$

$\log(1.125)=x\log(1.03)$

$\frac{\log(1.125)}{\log(1.03)}=x$

$3.98=x$

Approximately x=4 years.

Therefore, Option A is correct.