Question

Help me with these questions

Answer 1

Answer: a = 4, b = 163,422

Step-by-step 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)

$\frac{7003}{1920} = P_{0}$

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

Step-by-step 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

Step-by-step explanation:

$e^{-10} = \frac{1}{e^{10}}$

$ln(e^{-10}) = ln(\frac{1}{e^{10}})$

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

 0 = ln 1