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Anettt [7]
3 years ago
7

Plz help me!!!

Mathematics
1 answer:
Nadya [2.5K]3 years ago
8 0
To solve this we are going to use the exponential function: f(t)=a(1(+/-)b)^t
where
f(t) is the final amount after t years
a is the initial amount
b is the decay  or grow rate rate in decimal form
t is the time in years

Expression A 
f(t)=624(0.95)^{4t}
Since the base (0.95) is less than one, we have a decay rate here.
Now to find the rate b, we are going to use the formula: b=|1-base|*100%
b=|1-0.95|*100%
b=0.05*100%
b=5%
We can conclude that expression A decays at a rate of 5% every three months.

Now, to find the initial value of the function, we are going to evaluate the function at t=0
f(t)=624(0.95)^{4t}
f(0)=624(0.95)^{0t}
f(0)=624(0.95)^{0}
f(0)=624(1)
f(0)=624
We can conclude that the initial value of expression A is 624.

Expression B
f(t)=725(1.12)^{3t}
Since the base (1.12) is greater than 1, we have a growth rate here.
To find the rate, we are going to use the same equation as before:
b=|1-base|*100%
b=|1-1.12|*100
b=|-0.12|*100%
b=0.12*100%
b=12%
We can conclude that expression B grows at a rate of 12% every 4 months.

Just like before, to find the initial value of the expression, we are going to evaluate it at t=0
f(t)=725(1.12)^{3t}
f(0)=725(1.12)^{0t}
f(0)=725(1.12)^{0}
f(0)=725(1)
f(0)=725
The initial value of expression B is 725.

We can conclude that you should select the statements:
- Expression A decays at a rate of 5% every three months, while expression B grows at a rate of 12% every fourth months. 

- Expression A has an initial value of 624, while expression B has an initial value of 725.

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