6. Since 1992, the value of homes in a neighborhood has doubled every 16 years. The value of one home in the neighborhood was $$ 136, 500$ in 1992
a. What is the value of this home, in dollars, in the year 2000? Explain your reasoning.
b. Write an equation that represents the growth in housing value as a function of time in $t$ years since 1992.
c. Write an equation that represents the growth in housing value as a function of time in $d$ decades since 1992.
d. Use one of your equations to find the value of the home, in dollars, 1.5 decades after 1992.
(From Unit 4, Lesson 4.)
Algebra 2

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d. Substitute 1.5 decades into the equation c: $V (1.5) = 136, 500 \times 2^{\frac{10 \times 1.5}{16}}$ , which gives $V (1.5) = 136, 500 \times 2^{\frac{15}{16}} \approx $ 265, 967.66$ .

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Step 1 ：a. Since 2000 is 8 years after 1992, divide 16 years by 2 to get the half-growth period: $\frac{16}{2} = 8$ years. Multiply the home value in 1992 by 2 for half growth: $136, 500 \times 2 = $ 273, 000$ .

Step 2 ：b. $V (t) = 136, 500 \times 2^{\frac{t}{16}}$ where $V (t)$ is the value of the home in dollars and $t$ is the number of years since 1992.

Step 3 ：c. Since there are 10 years in a decade, replace $t$ with $10 d$ : $V (d) = 136, 500 \times 2^{\frac{10 d}{16}}$ , where $V (d)$ is the value of the home in dollars and $d$ is the number of decades since 1992.

Step 4 ：d. Substitute 1.5 decades into the equation c: $V (1.5) = 136, 500 \times 2^{\frac{10 \times 1.5}{16}}$ , which gives $V (1.5) = 136, 500 \times 2^{\frac{15}{16}} \approx $ 265, 967.66$ .

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