# Putting It Together: Exponential and Logarithmic Functions

At the start of this module, you were considering investing your inheritance possibly to save for retirement. Now you can use what you’ve learned to figure it out. The final value of your investment can be represented by the equation[latex]f(t)=Pe^{\large{rt}}[/latex]

where[latex]P[/latex] = the initial investment

[latex]t[/latex] = number of years invested

[latex]r[/latex] = interest rate, expressed as a decimal

Now remember that you had $10,000 to invest, so [latex]P=10,000[/latex]. Also recall that the interest rate was 3%, so [latex]r=0.03[/latex]. Let’s start with 5 years, so [latex]t=5[/latex].Start with the function: | [latex]f(t)=Pe^{\large{rt}}[/latex] |

Substitute P, r, and t: | [latex]f(5)=10,000e^{\large{0.03}{(5)}}[/latex] |

Evaluate: | [latex]f(5)=11,618.34[/latex] |

Now let’s look at 10 years, so [latex]t= 10[/latex].

Start with the function: | [latex]f(t)=Pe^{\large{rt}}[/latex] |

Substitute P, r, and t: | [latex]f(10)=10,000e^{\large{0.03}{(10)}}[/latex] |

Evaluate: | [latex]f(10)=13,498.59[/latex] |

Start with the function: | [latex]f(t)=Pe^{\large{tr}}[/latex] |

Substitute P, r, and t: | [latex]f(50)=10,000e^{\large{0.03}{(50)}}[/latex] |

Evaluate: | [latex]f(10)=44,816.89[/latex] |

[latex]t[/latex] | Interest rate | [latex]f(t)[/latex] |

5 | 0.03 | $11,618.34 |

10 | 0.03 | $13.498.59 |

50 | 0.03 | $44,816.89 |

## Licenses & Attributions

### CC licensed content, Original

- Putting It Together: Exponential and Logarithmic Functions.
**Authored by:**Lumen Learning.**License:**CC BY: Attribution.