Question

Graph the following exponential function, then answer the following questions:

`f\left(x\right)=12\cdot\left(1.17\right)^{x}`

Answer 1

is is increasing or decrease

Answer 2

what is the y intercept

Answer 3

To graph the exponential function f(x) = 12(1.17)^x, we can start by plotting a few points:

When x = -2:
f(-2) = 12(1.17)^-2 ≈ 12(0.5738) ≈ 6.8846
So one point is (-2, 6.8846)

When x = -1:
f(-1) = 12(1.17)^-1 ≈ 12(0.8547) ≈ 10.2564
So another point is (-1, 10.2564)

When x = 0:
f(0) = 12(1.17)^0 = 12
So another point is (0, 12)

When x = 1:
f(1) = 12(1.17)^1 ≈ 12(1.17) ≈ 14.04
So another point is (1, 14.04)

When x = 2:
f(2) = 12(1.17)^2 ≈ 12(1.3669) ≈ 16.4031
So the last point is (2, 16.4031)

Now, we can plot these points on a graph and see the shape of the exponential function.

After plotting the points and connecting them with a smooth curve, we can see that the graph of f(x) = 12(1.17)^x is continuously increasing as x increases. The graph starts below the x-axis, increasing rapidly and then continues to increase at a slower rate.

As x approaches negative infinity, the function approaches y = 0 but never actually touches the x-axis. As x approaches positive infinity, the function increases without bound.

Answer 4

The exponential function f(x) = 12(1.17)^x is continuously increasing as x increases. This can be seen from the graph we plotted earlier - as x increases, the value of the function f(x) also increases. The function never decreases as x increases, it only increases at a varying rate, with the rate of increase becoming smaller as x increases.

Answer 5

To find the y-intercept of the exponential function f(x) = 12(1.17)^x, we can plug in x = 0 into the function:

f(0) = 12(1.17)^0
f(0) = 12(1)
f(0) = 12

So, the y-intercept of the function is y = 12. This means that the graph intersects the y-axis at the point (0, 12).