MATH SOLVE

4 months ago

Q:
# Cells undergoing mitosis double with each cycle. A biologist has a sample containing 15 cells. Which graph and equation represents the number of cells after each cycle occurs?

Accepted Solution

A:

Answer:The equation is y = 15(2)^x , the graph is XStep-by-step explanation:* Lets talk about the exponential graph- The form of the exponential function is y = ab^x, where a ≠ 0, b > 0 , b ≠ 1, and x is any real number- It has a constant base b- It has a variable exponent x- The constant a is the beginning value * Lets solve the problem- The sample containing 15 cells∴ a = 15- The cells double with each cycle ⇒ means × 2 each cycle∴ b = 2- x is the number of cycles- y is the number of cells∴ The equation is y = 15(2)^x- From the graphs the answer could be X or Y* To know which one substitute the values of x to find the value of y# Figure X∵ y = 15(2)^x∵ x = 0∴ y = 15(2)^0 ∵ (2)^0 = 1 ⇒ any number to the power of 0 = 1 except the zero∴ y = 15(1) = 15∵ x = 1∴ y = 15(2)^1 = 15(2) 30- The graph has y = 30 when x = 1# In the Figure Y the value of y not equal 30 at x = 1∴ The answer is graph X* The equation is y = 15(2)^x , the graph is X