Question

eulers number, e practice
complete this assessment to review what youve learned. it will not count toward your grade.
dr. marie franklin observed that the approximate number of microbes in a petri - dish after t hours is given by the equation $a(t)=25e^{0.5t}$. how many microbes will be present in the dish after three hours? round your answer to the nearest whole number (1 point)
microbes
check answer remaining attempts: 3

Explanation:

Step1: Substitute t = 3 into the formula

Substitute \(t = 3\) into \(A(t)=25e^{0.5t}\), we get \(A(3)=25e^{0.5\times3}\).

Step2: Calculate the exponent value

First, calculate \(0.5\times3 = 1.5\). So \(A(3)=25e^{1.5}\).

Step3: Find the value of \(e^{1.5}\)

We know that \(e\approx2.71828\), then \(e^{1.5}\approx4.48169\).

Step4: Calculate the final result

Multiply 25 by the value of \(e^{1.5}\), \(A(3)=25\times4.48169 = 112.04225\).

Step5: Round to the nearest whole number

Rounding 112.04225 to the nearest whole number gives 112.

Answer:

112