Complete question :
Lower-than-expected demand for LCD TVs has spurred manufacturers to cut prices in recent years. The average price P of a 32-in. LCD TV t years after 2005 can be approximated by P(t) 1052(0.793), where t0 corresponds to 2005 a) What was the average price of an LCD TV in 2005? in 2009? in 2011?
Answer:
1052 ; 416.01 ; 261.61
Step-by-step explanation:
Given the price function :
P(t) = t0(0.793)^t
P(t) = 1052(0.793)^t
Price in 2005 = 1052
The average price of LCD in 2005 is t0
t - t0 = 2005 - 2005 = 0
P(0) = 1052(0.793)^0 ;
P(0) = 1052 * 1 =
Price in 2005 = 1052
Price in 2009 :
t = 2009 - 2005 = 4
P(t) = t0(0.793)^t
P(4) = 1052(0.793)^4
P(4) = 1052 * 0.39534 = 416.0145
Price of LCD in 2009 = 416.01
Price in 2011
t = 2011 - 2005 = 6
P(t) = t0(0.793)^t
P(6) = 1052(0.793)^6
P(6) = 1052 * 0.248679 = 261.6103
Price of LCD in 2009 = 261.61
Population growth is generally given by an exponential function,
<em>f</em>(<em>x</em>) = <em>a</em>*<em>b</em>^<em>x</em>, where <em>a</em> is the original population, <em>b</em> = 1 + the rate of growth (written as a decimal number), and <em>x</em> is the amount of time. In our case we have
<em>p</em>(1 + 0.065)<em>^</em>1<em>
</em>= <em>p</em>(1.065) = 1.065<em>p</em>
It equals 72. If you have a problem like this again first start with the brackets, and the parentheses inside the brackets (if there is any). Then move onto the others outside the brackets like other parentheses (if there is any)
