Answer:
See below
Step-by-step explanation:
<h3>Given</h3>
- Initial population at 8:00 AM
- 3000000
- Growth rate = 10% = 1.1 times per 20 min
<h3>Solution</h3>
<u>1. Table</u>
<em>Note. I am not sure what are the last 3 rows. Just added next 3 terms.</em>
- 8:00 ≡ G(0) ≡ 3000000 ≡ 3000000
- 8:20 ≡ G(1) ≡ 3000000 *1.1 ≡ 3300000
- 8:40 ≡ G(2) ≡ 3000000 *1.1^2 ≡ 3630000
- 9:00 ≡ G(3) ≡ 3000000 *1.1^3 ≡ 3993000
- 9:20 ≡ G(4) ≡ 3000000 *1.1^4 ≡ 4392300
<u>2. Population at 10:00</u>
- Time passed since 8:00 is 2 hours = 2*3*20 min = 6* 20 min
- Population = 3000000*1.1^6 = 5314683
<u>3. Function to reflect the population growth</u>
- G(x) = 3000000*1.1^x
- G(x) - is dependent variable, population of bacteria
- x - is independent variable, time increment of 20 min
<u>4. Population after 5 hours</u>
- 5 hours = 5*3*20 min = 15*20 min
- G(15) = 3000000*1.1^15 ≈ 12531745
Answer:
See explanation
Step-by-step explanation:
f(x) = -2lx-3| +1
1.lx-3|==>Translate the basic absolute value graph f(x)=|x| 3 units to the right
2. -lx-3| ==> Flip the graph over the x-axis
3. -2lx-3| ==> Double all the y-coordinates of the graph
4. -2lx-3| +1 ==> Translate the graph 1 unit up
I suppose you just have to simplify this expression.
(2ˣ⁺² - 2ˣ⁺³) / (2ˣ⁺¹ - 2ˣ⁺²)
Divide through every term by the lowest power of 2, which would be <em>x</em> + 1 :
… = (2ˣ⁺²/2ˣ⁺¹ - 2ˣ⁺³/2ˣ⁺¹) / (2ˣ⁺¹/2ˣ⁺¹ - 2ˣ⁺²/2ˣ⁺¹)
Recall that <em>n</em>ª / <em>n</em>ᵇ = <em>n</em>ª⁻ᵇ, so that we have
… = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)
… = (2¹ - 2²) / (2⁰ - 2¹)
… = (2 - 4) / (1 - 2)
… = (-2) / (-1)
… = 2
Another way to get the same result: rewrite every term as a multiple of <em>y</em> = 2ˣ :
… = (2²×2ˣ - 2³×2ˣ) / (2×2ˣ - 2²×2ˣ)
… = (4×2ˣ - 8×2ˣ) / (2×2ˣ - 4×2ˣ)
… = (4<em>y</em> - 8<em>y</em>) / (2<em>y</em> - 4<em>y</em>)
… = (-4<em>y</em>) / (-2<em>y</em>)
… = 2
