How to Write an Exponential Function Given a Rate and an Initial Value
Consider an example., Know the basic form.,Plug in the initial value for P and the rate for r. You will have f(t)=1,000(1.03)t/h. , Find h. Think about your equation.
Step-by-Step Guide
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Step 1: Consider an example.
Suppose a bank account is started with a $1,000 deposit and the interest rate is 3% compounded annually.
Find an exponential equation modeling this function. -
Step 2: Know the basic form.
The form for an exponential equation is f(t)=P0(1+r)t/h where P0 is the initial value, t is the time variable, r is the rate and h is the number needed to ensure the units of t match up with the rate. ,, Every year, the money increases by 3%, so every 12 months the money increases by 3%.
Since you need to give t in months, you have to divide t by 12, so h=12.
Your equation is f(t)=1,000(1.03)t/12.
If the units are the same for the rate and the t increments, h is always
1. -
Step 3: Plug in the initial value for P and the rate for r. You will have f(t)=1
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Step 4: 000(1.03)t/h.
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Step 5: Find h. Think about your equation.
Detailed Guide
Suppose a bank account is started with a $1,000 deposit and the interest rate is 3% compounded annually.
Find an exponential equation modeling this function.
The form for an exponential equation is f(t)=P0(1+r)t/h where P0 is the initial value, t is the time variable, r is the rate and h is the number needed to ensure the units of t match up with the rate. ,, Every year, the money increases by 3%, so every 12 months the money increases by 3%.
Since you need to give t in months, you have to divide t by 12, so h=12.
Your equation is f(t)=1,000(1.03)t/12.
If the units are the same for the rate and the t increments, h is always
1.
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Emily Parker
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