Question

Exponential Growth. A house is purchased for P1,000,000 in 2002. The value of the house is given by the exponential growth model A = 1,000,000e0.645t. Find t when the house would be worth P5,000,000.​

Answer 1

Answer:

a house is purchased for 1,000,000 in 2002. The value of the house is given by the exponential growth model A=1,000,000e^0.645t. Find t when the house would be worth 5,000,000

Answer 2

SOLUTION

GIVEN

A house is purchased for P1,000,000 in 2002.

The value of the house is given by the exponential growth model

$\sf A =1,000, 000 \: {e}^{0.645t}$

TO DETERMINE

Find t when the house would be worth P5,000,000.

EVALUATION

Here the exponential growth model is given by

$\sf A =1,000, 000 \: {e}^{0.645t}$

Now we have to t when A = 5,000,000

Putting A = 5,000,000 we get

$\sf 5,000, 000 =1,000, 000 \: {e}^{0.645t}$

$\sf \implies \: 1,000, 000 \: {e}^{0.645t} = 5,000, 000$

$\sf \implies \: \: {e}^{0.645t} = 5$

Taking logarithm in both sides we get

$\sf \implies \: 0.645t = ln \: 5$

$\sf \implies \: 0.645t = ln \: 5$

$\sf \implies \: 0.645t = 1.609$

$\sf \implies \: t = \dfrac{1.609}{0.645}$

$\sf \implies \: t \approx \: 2.5$

FINAL ANSWER

Hence the required value of t = 2.5

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