irections: Read each problem carefully, choose the correct model, then solve.
. Annual sales for a fast food restaurant are and are increasing at a rate of per year.
Use an exponential function to find the annual sales after 7 years.

Question

irections: Read each problem carefully, choose the correct model, then solve.
. Annual sales for a fast food restaurant are

and are increasing at a rate of

per year.
Use an exponential function to find the annual sales after 7 years.

UpStudy AI · Accepted Answer

To find the annual sales after 7 years, we can use an exponential function to model the growth of the sales.

Given:
- Initial annual sales: $$ \$650,000 $$
- Annual increase rate: $$ 4\% $$

The exponential function to model the growth of annual sales is given by:
$$ A(t) = A_0 \times (1 + r)^t $$
where:
- $$ A(t) $$ is the annual sales after $$ t $$ years
- $$ A_0 $$ is the initial annual sales
- $$ r $$ is the annual increase rate
- $$ t $$ is the number of years

Substitute the given values into the exponential function:
$$ A(t) = 650,000 \times (1 + 0.04)^t $$

Now, we need to find the annual sales after 7 years. Substitute $$ t = 7 $$ into the function:
$$ A(7) = 650,000 \times (1 + 0.04)^7 $$

Let's calculate the annual sales after 7 years using the exponential function.
Calculate the value by following steps:
- step0: Calculate:
  $$650000\left(1+0.04\right)^{7}$$
- step1: Add the numbers:
  $$650000\times 1.04^{7}$$
- step2: Convert the expressions:
  $$650000\left(\frac{26}{25}\right)^{7}$$
- step3: Simplify:
  $$650000\times \frac{26^{7}}{25^{7}}$$
- step4: Rewrite the expression:
  $$3125\times 208\times \frac{26^{7}}{25^{7}}$$
- step5: Rewrite the expression:
  $$5^{5}\times 208\times \frac{26^{7}}{5^{14}}$$
- step6: Reduce the numbers:
  $$208\times \frac{26^{7}}{5^{9}}$$
- step7: Multiply:
  $$\frac{208\times 26^{7}}{5^{9}}$$
The annual sales after 7 years will be approximately $$ \$855,355.66 $$.
After 7 years, the annual sales will be approximately \$855,355.66.

irections: Read each problem carefully, choose the correct model, then solve.
. Annual sales for a fast food restaurant are and are increasing at a rate of per year.
Use an exponential function to find the annual sales after 7 years.

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irections: Read each problem carefully, choose the correct model, then solve. . Annual sales for a fast food restaurant are and are increasing at a rate of per year. Use an exponential function to find the annual sales after 7 years.

Upstudy AI Solution

Answer

Solution

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Latest Algebra Questions

irections: Read each problem carefully, choose the correct model, then solve.
. Annual sales for a fast food restaurant are and are increasing at a rate of per year.
Use an exponential function to find the annual sales after 7 years.