Explanation

Since the population growth is exponential, the population P can be modeled as:

P = P0 x (1 + r)^t

where P0 is the initial population, r is the growth rate, and t is the time (in years).

Given that the initial population P0 = 20 and the population grew to 25 after 2 years, we can find the growth rate r:

25 = 20 x (1 + r)^2

Dividing both sides by 20:

1.25 = (1 + r)^2

Taking the square root:

1 + r = √1.25 = 1.125

Subtracting 1 from both sides:

r = 0.125

Now we can write the exponential growth function:

P = 20 x (1 + 0.125)^t

P = 20 x (1.25)^t

Explanation

To find |f(1)|, we need to evaluate the function f(x) = -3(x^2) - 2(x) + 1 at x = 1.

f(1) = -3(1^2) - 2(1) + 1

= -3(1) - 2(1) + 1

= -3 - 2 + 1

= -4

Now, we need to find the absolute value of f(1):

|f(1)| = |-4| = 4

Explanation

Combine like terms:

$$(49-3b+5c)+(-50+4b-c)$$

1. Combine constants: $49 - 50 = -1$
   
2. Combine $b$-terms: $-3b + 4b = b$
   
3. Combine $c$-terms: $5c - c = 4c$
   

Final expression:

$$-1+b+4c$$

Explanation

We know that:

x × x = x²

Reciprocal of x = 1/x

According to the problem:

(x × x) ÷ (1/x) = 18/26 × 27

Simplifying the equation:

x² ÷ (1/x) = 18/26 × 27

x³ = 18/26 × 27

Now, let's solve for x:

x³ = 486/26

x³ = 18.69 (approximately)

x = ∛(18.69) ≈ 2.67

Explanation

Let's evaluate the expressions using the given definition of a * b:

3 * 4 = 3 + 4 + (3)(4) = 3 + 4 + 12 = 19

2 * 3 = 2 + 3 + (2)(3) = 2 + 3 + 6 = 11

Now, let's subtract:

3 * 4 - 2 * 3 = 19 - 11 = 8