Question

An evergreen nursery usually sells a certain shrub after 6 years of growth and shaping. The growth rate during those 6 years is approximated by dh/dt=3.5t+7 where t is the time in years and h is the height in centimeters. The seedlings are 15 centimeters tall when planted (t=0) . Find the height after t years. @phi

Answer 1

1. growth rate is approximated by dh/dt function. t = 6, so next we approximate the growth rate across the time span

2. find the growth rate dh/dt when t = 6. dh/dt = 28 cm / year

3. the plant is initially 15 cm, but add 28cm per year

4. evaluate function from step 3 at h(6).

This is a bit of an odd question so a second opinion would be nice

Answer 2

@hayatabz1 make sure you look at the attached file

do we have an answer key to this question, can we verify the result?

Answer 3

thats not in the options... the options are
@stamp

Answer 4

a.11 b.23 c.47 d.52 e.29

Answer 5

@stamp

Answer 6

idk man are you sure those answer choices are correct

Answer 7

all i can say at this point is

find the height.

cm = cm/year * years

h = dh/dt * t

Answer 8

h = (3.5t + 7)*t

h = 3.5t^2 + 7t

Answer 9

idfk

Answer 10

oh my god sorry those were the wrong choicees these are the choices..
@stamp

Answer 11

@stamp

Answer 12

You have a differential equation
\[ \frac{dh}{dt}= 3.5t+7 \]
we can write this as
\[ dh = 3.5 t + 7 dt\]
now integrate both sides
\[ \int dh = \int 3.5t + 7\ dt \]
can you integrate this?

Answer 13

yes 1.75t^2+6t+C?

Answer 14

7t*

Answer 15

@phi

Answer 16

is C=15?

Answer 17

so it would be h(t)=1.75^2+7t+15?

Answer 18

@phi

Answer 19

yes 1.75t^2+6t+C?

to be complete we get
h + c1 = 1.75t^2+6t+c2
but c1 and c2 are unknown constants, so we can write this as
h = 1.75t^2+6t+c2-c1

but c2-c1 is just an unknown constant, so just write it as
h = 1.75t^2+6t+C

(just like what you got, but with the gory details)

to find C, replace t with 0 (because at t=0 we know h=15)
15= 0+0+C
C= 15

now you have the full equation
h= 1.75t^2+6t+15

Answer 20

thank you very much you are writing 6t shouldnt it be 7t though? @phi

Answer 21

yes, I meant 7t

Answer 22

I copied and pasted your answer, and did not notice the 6t instead of 7 t

Answer 23

*before you fixed it

Answer 24

oh ok thank you @phi