Answer: a = 4, b = 163,422
Step-by-step explanation:
[tex]P = P_{0} e^{kt}[/tex] 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)
[tex]P = P_{0} e^{kt}[/tex] need to solve for P₀
[tex]7003 = P_{0} e^{(.21)(36)}[/tex]
[tex]7003 = P_{0} e^{7.56}[/tex]
7003 = P₀ (1920)
[tex]\frac{7003}{1920} = P_{0}[/tex]
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)
[tex]P = P_{0} e^{kt}[/tex] need to solve for P₀
[tex]P = 7003 e^{(.21)(15)}[/tex]
[tex]P = 7003 e^{3.15}[/tex]
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:
[tex]e^{-10} = \frac{1}{e^{10}}[/tex]
[tex]ln(e^{-10}) = ln(\frac{1}{e^{10}})[/tex]
-10 = ln 1 - 10 log rules say division is subtraction
0 = ln 1
