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Jinesha
23.02.2021 •
Mathematics
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Answers on questions: Mathematics
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Ответ:
A.) 9
B.) 9
C.) It represents a slope or gradient which is equal to 0.9
Step-by-step explanation:
A.) You are given the equation to show the radius of the algae, f(d), in mm, after d days: f(d) = 9(1.04)^d
To find the domain, substitute 12.81 mm for function f(d) in the given equation.
12.81 = 9(1.04)^d
Divide both sides by 9
(1.04)^d = 12.81/9
(1.04)^d = 1.423333
Log both sides
Log (1.04)^d = log ( 1.423333)
d Log(1.04) = log(1.42333)
Make d the subject of formula
d = log(1.4233) / log(1.04)
d = 9
Therefore, the reasonable domain to plot the growth function is 9
B.) The y - intercept of the graph of the function f(d) is the initial radius of the algae which is represented by 9
C.) From the given function
F(d) = 9(1.04)^d
Substitute d for 3 and 9
The given value for f(d) when the domain d = 9 is 12.81
When d = 3
Substitute d for 3 into the formula
F(d) = 9(1.04)^3
F(d) = 9 × 1.124864
F(d) = 10.12
the average rate of change of the function will be
M = ( 10.12 - 12.81 ) / ( 3 - 6 )
M = - 2.686 / - 3
M = 0.895
M represent the slope or the gradient of the function.