An investor is deciding between two options for a short-term investment. One option has a return R, in dollars, t months after investment, and is modelled by the equation `R=100(3^t)`. The other option has a return R, in dollars, t months after investment, and is modeled by the equation R=350 t. After 4 months, how much less in the return given by the linear model than the return given by the exponential model?

Options

A. 1400
B. 4050
C. 6700
D. 8100

Answer

To solve the problem, we need to calculate the returns from both the exponential and linear models after 4 months and then find the difference between them.

### Step-by-Step Solution:

1. **Calculate the return from the exponential model:**
The return \( R_E \) from the exponential model is given by the equation:
\[ R_E = 100 \cdot (3^t) \]
Substituting \( t = 4 \):
\[ R_E = 100 \cdot (3^4) \]
Now, calculate \( 3^4 \):
\[ 3^4 = 81 \]
Therefore,
\[ R_E = 100 \cdot 81 = 8100 \]

2. **Calculate the return from the linear model:**
The return \( R_L \) from the linear model is given by the equation:
\[ R_L = 350 \cdot t \]
Substituting \( t = 4 \):
\[ R_L = 350 \cdot 4 = 1400 \]

3. **Find the difference between the returns:**
We need to find how much less the return from the linear model is compared to the return from the exponential model:
\[ \text{Difference} = R_E - R_L \]
Substituting the values we calculated:
\[ \text{Difference} = 8100 - 1400 = 6700 \]

### Final Answer:
The return given by the linear model is $6700 less than the return given by the exponential model after 4 months.

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