What’s the graph function f(x) =4(1.5)^x

See below.

Step-by-step explanation:

Step 1. Find any zeroes.

(a) y-intercept

y = 4(1.5)^x     Let x = 0

  = 4(1.5)⁰

  = 4 × 1

  = 4

We have a point at (0,4).

(b) x-intercept

    y = 4(1.5)^x     Let y = 0

    0 = 4(1.5)^x     Divide each side by 4

    0 = (1.5)^x        Take the log of each side

log0 = xlog1.5

log(0) is undefined. There is no x-intercept.

Step 2. Identify any asymptotes

y = 4(1.5)^x

y can never be negative, so the x-axis is an asymptote.

Step 3. Plug in and plot a few points

Here's a table of a few points.

 x      y  

-6     0.4

-4     0.8

-2     1.8

-1     2.7

0    4.0

1     6.0

2    9.0

4  20.3

6  45.6

Step 4. Check the end behaviour.

y = 4(1.5)^x

As x ⟶ ∞, y ⟶ ∞.

As x ⟶ -∞, y ⟶ 0 .

Step 5. Draw a smooth line through the points.

Your graph should look something like the one below.

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.