i need help with this.
In 1994, the number of cassette singles shipped was 81.1 million. In 1997, that number dropped to 42.2 million. Write an equation that gives the number of cassettes shipped, y, in terms of the year, t. Let t=4 represent 1994.
how do yu do this ? thanks (:
y=(-12.97t + 132.97)*10^6
-So for 1999 (t=9) this gives 16.27 million cassettes shipped.
*Sorry if its incorrect (this was my best answer).
To write an equation that gives the number of cassettes shipped, y, in terms of the year, t, we can start by looking at the given information. We know that in 1994 (when t = 4), the number of cassette singles shipped was 81.1 million, and in 1997 (when t = 7), that number dropped to 42.2 million.
To find the equation, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope, m, which represents the rate of decrease. We can calculate the change in the number of cassette singles shipped (Δy) divided by the change in years (Δt).
Δy = 42.2 million - 81.1 million = -38.9 million
Δt = 7 - 4 = 3
m = Δy / Δt = -38.9 million / 3 ≈ -12.97 million
Now that we have the slope, we need to find the y-intercept, b. We can substitute the t-value of one of the given points (t = 4, y = 81.1 million) into the slope-intercept form equation and solve for b.
y = mx + b
81.1 million = -12.97 million x 4 + b
81.1 million = -51.88 million + b
To isolate b, we can add 51.88 million to both sides of the equation:
81.1 million + 51.88 million = b
133.98 million = b
Now that we have the slope (m = -12.97 million) and the y-intercept (b = 133.98 million), we can write the equation:
y = -12.97 million t + 133.98 million
So, the equation that represents the number of cassettes shipped, y, in terms of the year, t, is y = -12.97 million t + 133.98 million.