The graph of y = 3(10)^x − 1 is shown. What are the x-intercept (rounded to the nearest tenth) and the horizontal asymptote, and do they represent exponential growth or decay?
+129849 Here's the graph : https://www.desmos.com/calculator/qgngrhqfqf
To find the x-intercept....let y = 0 and solve for x
0 = 3(10)^x - 1 add 1 to both sides
1 = 3(10)^x divide both sides by 3
1/3 = 10^x take the log of both sides
log (1/3) = log(10)^x and we can write
log(1/3) = x log(10) log(10) = 1 so we can ignore this
log(1/3) = x = about -0.48
The horizontal asymptote is y = -1
This is a growth curve because as x grows larger, y grows larger
