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## Algebra 2 (Eureka Math/EngageNY)

### Unit 3: Lesson 10

Topic D: Lessons 23-24: Solving exponential models

# Exponential model word problems

## Problem

A culture of bacteria starts with 50 bacteria and increases exponentially.
The relationship between B, the number of bacteria in the culture, and d, the elapsed time, in days, is modeled by the following equation.
$B=50\cdot 10\^{{\frac{d}2}}$
In how many days will the number of bacteria in the culture reach 800, comma, 000?
Give an exact answer expressed as a base-ten logarithm.
days
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