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____ [38]
3 years ago
14

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 ye

ars, how many years will it take the house to be worth approximately $225,000?
A) 4 years
B) 5 years
C) 6 years
D) 7 years
Mathematics
2 answers:
Elza [17]3 years ago
6 0
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
Delicious77 [7]3 years ago
4 0

Answer:

Option A - 4 years

Step-by-step explanation:

Given : Mike and Beatrice purchase a house for $200,000. If the equation V = 200000(1.03)^x 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.

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