the regression calculator. be sure to choose a good window setting!\nthe data show that the population of…

the regression calculator. be sure to choose a good window setting!\nthe data show that the population of lily pads has an increasing growth rate.\ncomplete\nan exponential function would be most suitable to model these data.\ncomplete\nthe general form of an exponential function is y = ab^x. use the regression calculator to find the values of a and b for the water lily population growth. round to the nearest thousandth.\na = and b = \ndone

the regression calculator. be sure to choose a good window setting!\nthe data show that the population of lily pads has an increasing growth rate.\ncomplete\nan exponential function would be most suitable to model these data.\ncomplete\nthe general form of an exponential function is y = ab^x. use the regression calculator to find the values of a and b for the water lily population growth. round to the nearest thousandth.\na = and b = \ndone

Answer

Explanation:

Step1: Recall exponential - regression concept

In an exponential function (y = ab^{x}), when (x = 0), (y=a\times b^{0}=a). From the table, when (x = 0) (number of days), (y = 4) (number of water - lilies). So (a = 4).

Step2: Use another data - point to find (b)

We know the function is (y = 4b^{x}). Let's use the data - point ((x = 5,y = 7)). Substitute into the function: (7=4b^{5}). Then (b^{5}=\frac{7}{4}), and (b=\left(\frac{7}{4}\right)^{\frac{1}{5}}). Calculate (b=\left(\frac{7}{4}\right)^{\frac{1}{5}}=\sqrt[5]{\frac{7}{4}}\approx1.124).

Answer:

(a = 4) and (b\approx1.124)