[math]2^{10}\div2^7[/math]
[size=150]Here are some equations. Find the solution to each equation using what you know about exponent rules. Be prepared to explain your reasoning.[/size][br][br][math]9^?\cdot9^7=9^7[/math]
[math]\frac{9^{12}}{9^?}=9^{12}[/math]
What is the value of [math]5^0[/math]? [br][br]
What about [math]2^0[/math]?
[size=150]We know, for example, that [math]\left(2+3\right)+5=2+\left(3+5\right)[/math] and [math]2\cdot\left(3\cdot5\right)=\left(2\cdot3\right)\cdot5[/math]. The grouping with parentheses does not affect the value of the expression.[br][/size][br][size=100]Is this true for exponents? That is, are the numbers [math]2^{\left(3^5\right)}[/math] and [math]\left(2^3\right)^5[/math] equal? If not, which is bigger? [/size]
Which of the two would you choose as the meaning of the expression [math]2^{3^5}[/math] written without parentheses?
Write an expression to show how to find the number of bacteria after each hour listed in the table.
Write an equation relating [math]n[/math], the number of bacteria, to [math]t[/math], the number of hours.[br]
[size=150][size=100]Use your equation to find [math]n[/math] when [math]t[/math] is 0. [/size][/size]What does this value of [math]n[/math] mean in this situation?[br]
[size=150]In a different biology lab, a population of single-cell parasites also reproduces hourly. An equation which gives the number of parasites, [math]p[/math], after [math]t[/math] hours is [math]p=100\cdot3^t[/math]. [/size][br]Explain what the numbers 100 and 3 mean in this situation.[br]
On the graph of [math]n[/math], where can you see each number that appears in the equation?[br]
On the graph of [math]p[/math], where can you see each number that appears in the equation?[br]