Which are monomials?
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The question is incomplete. Here is the complete question.
Uninhibited growth can be modeled by exponential functions other than . for example, if an initial population P₀ requires n units of time to triple, then the function
models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.
a) If the population triples in 30 days, and 50 insects are present initially, write an exponential function of the form that models the population.
b) What will the population be in 47 days?
c) When wil the population reach 750?
d) Express the model from part (a) in the form .
Answer: a)
b) P(t) = 280 insects
c) t = 74 days
d)
Step-by-step explanation:
a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is
b) In t = 47 days:
P(47) = 280
In 47 days, population of insects will be 280
c) P(t) = 750
Using the property <u>Power</u> <u>Rule</u> of logarithm:
t = 74
To reach a population of 750 insects, it will take 74 days
d) To express the population growth into the described form, determine the constant k, using the following:
A(t) = 3A₀ and t = 30
Use Power Rule again:
k = 0.037
Equation for exponential growth will be:
Answer:
m∠CAB = 66°
m∠CAD = 24°
Step-by-step explanation:
<em>m∠CAB</em>
The given parameters are;
The measure of arc m = 228°
The diameter of the given circle =
The tangent to the circle =
The measure of m∠CAB and m∠CAD = Required
By the tangent and chord circle theorem, we have;
m∠CAB = (1/2) × m
However, we have;
m + m
= 360° the sum of angles at the center of a circle is 360°
∴ m = 360° - m
Which gives;
m = 360° - 228° = 132°
m = 132°
Therefore;
m∠CAB = (1/2) × 132° = 66°
m∠CAB = 66°
<em>m∠CAD</em>
Given that is the diameter of the given circle, we have
The tangent, , is perpendicular to the radius of the circle, and therefore
is also perpendicular to the diameter of the circle
∴ m∠DAB = 90° which is the measure of the angle formed by two perpendicular lines
By angle addition property, we have;
m∠DAB = m∠CAB + m∠CAD
∴ m∠CAD = m∠DAB - m∠CAB
By substitution, we have;
m∠CAD = 90° - 66° = 24°
m∠CAD = 24°