Respuesta :
Answer:
This is the actual steps and answer.
Step-by-step explanation:
\text{Exponential Functions:}
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }5000
a=starting value = 5000
r=\text{rate = }4\% = 0.04
r=rate = 4%=0.04
\text{Exponential Growth:}
Exponential Growth:
b=1+r=1+0.04=1.04
b=1+r=1+0.04=1.04
\text{Write Exponential Function:}
Write Exponential Function:
y=5000(1.04)^x
y=5000(1.04)
x
Put it all together
\text{Plug in time for x:}
Plug in time for x:
y=5000(1.04)^{7}
y=5000(1.04)
7
y= 6579.6589
y=6579.6589
Evaluate
y\approx 6580
y≈6580
round
The population after 7 years at the rate of 4% growth every year would be 6580.
What is the formula for exponential growth?
Exponential growth is a function that grows or decays at a constant percent rate.
The formula used is [tex]y = b(1 + r)^ t[/tex]. where, y is the exponential growth function, b is the initial amount, r rate, and t time interval.
From the information given,
b = 5000
r = 4% = 4/100
= 0.04
t = 7 years
Therefore
[tex]y = b(1 + r)^ t[/tex]
[tex]y = 5000(1 + 0.04)^7[/tex]
[tex]y = 5000(1.04)^7[/tex]
y = 6580
Thus, The population after 7 years at the rate of 4% growth every year would be 6580.
Learn more about exponential growth;
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