Question
Find the 𝑥 and 𝑦-intercepts. Show all calculations of 𝑦 = 3(2)^𝑥+1 − 12
Answers
GPT 3.5
To find the x-intercept, set y = 0 and solve for x.
0 = 3(2)^x + 1 - 12
3(2)^x + 1 = 12
3(2)^x = 11
(2)^x = 11/3
x = log2(11/3)
x ≈ 1.409
To find the y-intercept, set x = 0 and solve for y.
y = 3(2)^0 + 1 - 12
y = 3*1 + 1 - 12
y = 3 - 11
y = -8
Therefore, the x-intercept is approximately 1.409 and the y-intercept is -8.
0 = 3(2)^x + 1 - 12
3(2)^x + 1 = 12
3(2)^x = 11
(2)^x = 11/3
x = log2(11/3)
x ≈ 1.409
To find the y-intercept, set x = 0 and solve for y.
y = 3(2)^0 + 1 - 12
y = 3*1 + 1 - 12
y = 3 - 11
y = -8
Therefore, the x-intercept is approximately 1.409 and the y-intercept is -8.