Question

Help me with these questions

Answer 1

Answer: a = 4, b = 163,422

Explanation:

`P = P_(0) e^(kt)` P is the new population, P₀ is the initial population, k is the growth rate, t is the time elapsed.

Part a) What do we know?

P = 7003

P₀ = unknown

k = .21 (converted 21% into a decimal)

t = 36 yrs (2006 - 1970)

`P = P_(0) e^(kt)` need to solve for P₀

`7003 = P_(0) e^((.21)(36))`

`7003 = P_(0) e^(7.56)`

7003 = P₀ (1920)

`(7003)/(1920) = P_(0)`

3.6 = P₀

rounded to the nearest whole number = 4

Part b) What do we know?

P = unknown

P₀ = 7003

k = .21 (converted 21% into a decimal)

t = 15 yrs (2021 - 2006)

`P = P_(0) e^(kt)` need to solve for P₀

`P = 7003 e^((.21)(15))`

`P = 7003 e^(3.15)`

P = 7003(23.33)

P = 163,422.46

rounded to the nearest whole number = 163,422

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Answer: 2, -1

Explanation:

eˣ² = eˣ * e²

eˣ² = eˣ⁺²

x² = x + 2

x² - x - 2 = 0

(x - 2)(x + 1) = 0

x - 2 = 0 or x + 1 = 0

x = 2 or x = -1

Check both answer for validity:

eˣ² = eˣ⁺²

e⁴ = e⁴ or e¹ = e¹

TRUE TRUE

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Answer: 0 = ln 1

Explanation:

`e^(-10) = (1)/(e^(10))`

`ln(e^(-10)) = ln((1)/(e^(10)))`

-10 = ln 1 - 10 log rules say division is subtraction

0 = ln 1