1. decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. f(x) = 7.2 ⋅ 1.08^x a. exponential growth function; 8% b. exponential decay function; 108% c. exponential growth function; 108% d. exponential growth function; 0.08% 2. decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. f(x) = 2034 ⋅ 0.9939^x a exponential growth function; 0.0061% b exponential decay function; -0.61% c exponential growth function; -0.61% d exponential decay function; 0.0061% 3. find the exponential function that satisfies the given conditions: initial value = 30, increasing at a rate of 13% per year a f(t) = 30 ⋅ 1.13t b f(t) = 13 ⋅ 1.13t c f(t) = 30 ⋅ 0.13t d f(t) = 30 ⋅ 13t 4. find the exponential function that satisfies the given conditions: initial value = 70, decreasing at a rate of 0.5% per week a f(t) = 0.5 ⋅ 0.3t b f(t) = 70 ⋅ 1.005t c f(t) = 70 ⋅ 0.995t d f(t) = 70 ⋅ 1.5t

1. The correct option is a.

2. The correct option is b.

3. The correct option is a.

4. The correct option is c.

Step-by-step explanation:

A general exponential function is defined as

It can also written as

(For growth) or   (For decay)

where, a is initial value, b is growth factor.

If 0<b<1, then f(x) is a decay function, if b>1, the f(x) is growth function.

(1).

The given function is

Here, the initial value is 7.2 and growth factor is 1.08.

Growth factor is greater than 1, so f(x) is exponential growth function and percentage rate of growth is

Therefore the correct option is a.

(2)

The given function is

Here, the initial value is 2034 and growth factor is 0.9939.

Growth factor is less than 1, so f(x) is exponential decay function and percentage rate of growth is

Therefore the correct option is b.

(3)

Initial value = 30, increasing at a rate of 13% per year

a=30, r=0.13.

The required function is

Substitute a=30 and r=0.13.

Therefore the correct option is a.

(4)

Initial value = 70, decreasing at a rate of 0.5% per week

a=70, r=0.005

The required function is

Substitute a=70 and r=0.005.

Therefore the correct option is c.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

answer: 5

step-by-step explanation: